hey my dear neat Warriors welcome to the motion in the straight line session your chapter number two of your ncrt and also a very important chapter from your obviously neat perspective and welcome to the Super Six series and in this neat Super 6 series we are doing all the high weightage chapters first and all the essential chapters first and also helping you clear the backlogs for both need 2024 and if you are a ne25 student you can also watch it right so our Target is 700 plus and that's the quality of content that's the kind of content that you'll be getting in these sessions why are these ncrt lines plus pyqs plus the theory notes plus the quizzes everything after the class you'll be getting good morning good morning everyone nice to see all of you uh capto are you busy since J is closed very very very busy Sarat trust me on this this I am feeling so sleepy right now because I came home very late the entire day was just full of sessions straight almost like 10 hours classes and obviously paper solving yes but uh because I have to meet you all luckily today is uh a break in between the J sessions so that's the reason why I thought I should take the classes again for the next 4 days I'll be busy but I will be back again on uh Friday or Saturday for your next class of oscillations okay so watch every lecture because I'm taking a lot of effort and uh I'm coming over here shuffling between so many classes okay thank you so much for liking the video and if you have not yet subscribed to the vantu N English Channel do that we are I think close to 150k subscribers let's make this channel grow really big in the last just 1 month around we have you know uh I think we have added around 8,000 people roughly speaking speaking so let's take this a notch higher let's make this channel big and let's make this the number one which is already number one but let's make it even bigger number one channel in the country for all the need aspirants in English medium right so let's 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particular Victory mock test in case you haven't done that yet please do that right a right now okay is there right in the description box over here Victory mock test just click on this just click on this you will see okay you will get everything and you can see this QR code scan this QR code for getting the complete syllabus details what is the schedule anything else you want to ask you will get it right over here okay the entire mock test syllabus everything is there in this QR code click enroll now enter your details you'll be able to buy it it's 0 rupees today from tomorrow it will be $9.99 share it with your friends share it in the communities put it up in the status talk about it to your colleagues your classmates everyone okay because after this you will feel very bad if you have not bought this so let's start with position then we are going to go to displacement velocity acceleration some part of calculus and graphs kinematic equations Free Fall that is the flow of the chapter today okay hello Hindu hello Ranjit nice to see you all hello SEL Rupa thank you for all the hearts thank you uh for the white heart sight hello abav hello ranita hello monei hello hello Dr Sid nice to see you Jagdish next week Motion in the plane yes yashwant definitely yep thank you glad you like the ncrt line by line session yes another session happening on this Friday now when you go out to meet your friend this is you who has gone to meet your friend okay you say that you have gone to meet your friend but but actually you know this pandu is meeting Champa this pandu is meeting Champa then your mom calls you mom calls you and ask where are you where are you that means your mom is asking what is your position your mom is asking what is your position so you'll say I'm at my friend's place or I'm in the street I'm in the next building or I'm just in the library I'm in the uh whatever I'm eating some hot hot vas whatever you can say that but if you're more a bit more of a physics student you'll be like uh Hey listen mom my U position is x coordinate is 2 km my y coordinate is 1.5 km and I'm on the ground level only so there is no Zed coordinate so my Z coordinate is 0 km and considering a point at as the origin which is your home so your origin is your home so with the origin as the home taking each direction as this taking North direction as that taking South direction as another axis these are my coordinates so when a position is asked you are referring to the coordinates with respect to the origin isn't that right everybody agree with this but yeah if you give such an answer to your mom you will get one projectile motion and that projectile motion is nothing but your flying slipper you will get a nice flying slipper and the range is adjusted in such a way it might just Land close to the face or maybe at the back or maybe uh in the front also these these things might happen correct yes j25 can also watch ne25 can also watch definitely so position means where position means where are you and it is expressed generally in coordinates but we are talking about Motion in 1 D so we are talking about one dimensional motion then there is also two dimensional motion then there is also three dimensional motion Motion in 1 d means Motion in Wy means a pandu can only go straight forward or backward can move like this or like this or a pandu is going up or down pandu is going just up or down these are examples of ond motion 2D motion examples will be your flying slipper have you ever seen a flying slipper or a duster coming towards you or a chalk coming towards you in the school maybe so that is a two-dimensional motion or or you have gone mad you have gone crazy or gone tensed and you are holding a book just before the exam night and you're walking here and there randomly you're walking here then you're going here then you're going like this so this is also two- dimensional motion right and in threedimensional motion example will be a bird which is flying or an aeroplane a bird which is flying or an aeroplane which is there correct an aeroplane so when an aeroplane flies it goes like this like this it might go like that so it's a threedimensional motion in this chapter we are just focusing our attention on one dimensional motion on one dimensional motion hello vikran good morning now when we talk about onedimensional motion and we are referring to the position we either give only the x coordinate if the particle is going on the x-axis if the particle is going up and down then maybe we'll be just giving the y coordinate correct so only one coordinate will be involved and position is where are you where means direction is involved obviously when direction is involved it is a vector quantity what is it my dear Warriors it's a vector quantity because it has Direction associated with it and it also has magnitude it has direction as well as magnitude that's the reason why it is a vector quantity usually you will Express position in meters I am 5 m away I'm 20 M away I'm 79 M away you can also Express in kilometers ctime millimeters and so much more but meters is the standard SI unit correct and when an object is at rest its Position will not change imagine have you seen a donkey have you seen a donkey on the road this is a donkey imagine this is a donkey this is a donkey okay what does a donkey do whole day the donkey basically always stays at rest the donkey always stays at rest so if one person has taken this as the origin this as the y- axis this as the x-axis and if the donkey's position from the origin is 25 M even after 1 hour even after 2 hours even after 10 hours the donkey just standing there looking like this doing nothing like a fool it is looking so the position of that donkey the position of that donkey I will say it is 25 M and it is not changing it is basically constant it is basically constant everybody with me on this understood clear yes very good very good but if things move obviously the position will keep on changing the value of x will not remain constant so just imagine this again if I take this as my x-axis this is my origin and let's say we have a pandu who is very excited maybe he first goes here then goes here then again comes back over here Etc maybe initially he was here maybe at T is equal to 2 seconds he was here maybe at T is equal to 5 seconds he is here so what pandu has done is pandu has gone here and then pandu has come over here from 0 to 2 seconds he went here and from 2 to 5 seconds he came here so pandu is moving along the onedimensional motion so here obviously X is not a constant X is not a constant everybody understood this point everybody understood this point Paka Clearo very good awesome whenever T is equal to 0 whenever T is equal to 0 what does it mean whenever T is equal to 0 what does it mean you have just started seeing it you have just started calculating it you just started the event that means it is just initial it is just initial so T is equal to Z means you just started it it's just the initial Condition it's just initial situation so if they ask you initial position you see when timer was Zero where was pandu when timer was Zero where was pandu means initial position is that right everybody with me very good excellente now sometimes our position can be given in a tabular form or in an equation form in a tabular form or in a equation form example example X is given as example X is given as let's say T Cub X is given as T Cub meaning what you tell me the time I will tell you the position this is tabular form from equation how you tell me that time I will tell you the position very straightforward let's say initially when time was 0o substitute time as 0 0 cube is 0 so position is zero that means you are at the origin when time was 1 second when time was 1 second substitute time as 1 1 cube is basically nothing but one only substitute time as 2 seconds when time is 2 2 cube is nothing but 8 right when time is 3 seconds 3 Cub is nothing but 27 is nothing but 27 so whatever I written over here is the equation of the motion it is nothing but the equation of the motion whatever I have written here is nothing but the different positions different positions in a tabular form in a tabular form is that right in a tabular form at the same time you can also show this you can also show this in a visualized way in a visualized way something like this where you know this is my x- Axis this is my origin and at Time Zero I was at origin that means I was here that means I was here at T is equal to 0 I was here at T is equal to 0 at T is equal to 1 I was at 1 M at T is equal to 1 I was at 1 M at T is equal to 2 I was at 8 m 8 m is somewhere here so this is at T is equal to 2 at T is equal to 3 I was at 20 seven maybe it is here so this is how pandu is moving first he was here then here then here then here then here his is like accelerating isn't it crazy guys are you able to visualize this very nice very nice this is another way the Fourth Way can anybody tell me the fourth way of seeing this information if you're smart enough I think you will be able to figure it out and let me tell you you already know the answer yes kushy you are going to have the weekly mock test in the form of in the form of these Victory mock tests because these Victory mock tests are you know even better and the best part is they are with the latest syllabus and also they have been prepared by our experts again and we want you to have a proper schedule for the next 2 months so there is no tension in your head okay you know what is the plan for the third week or fourth week of March also so this is a complete mock tests which you're going to get till the end of the March absolutely free of cost so please make use of it and you cannot give three four mock tests on one single day please understand that also yes very good B that is the graph exactly so graph that means imagine this is time this is time this is position or basically X this is position or basically X then then I can show it graphically also at zero it is zero so this point at one it is one so at 1 second it is exactly 1 okay at two it is eight at two it is basically 8 so 0 0 1 1 at two it is basically 8 at three it is 27 Oh my God it goes there so the if I join all these point it becomes like a curve it becomes like a curve isn't that right it's a curve so so many ways of visualizing just the motion so many ways of just visualizing just the motion how many of you never knew that there were four ways of visualizing motion or interpretating motion maybe you might have learned this independently but I think now you understand what this equation means in tabular form in graphical form in visualized form or just equation form all these are very very interesting so this was your graphical form this was your graphical form that we just saw and this one over here this was how it will actually move this was actually visualized this was actually visualized you're actually showing the motion you know over here right very very interesting Perfecto perfecto so we have seen that now let's move on to distance and displacement distance and displacement so imagine let's carry forward our story pandu our pandu was meeting Champa over here this is Champa this is pandu right so pandu's Mom asked where are you pandu said I'm with Champa mom said do you want a fly slipper pandu said no so Mom said come back home immediately so what did pandu do immediately he started moving immediately he started moving so let's say pandu immediately he realized oh I have to pick up some potatoes mom had asked me to bring potatoes but I met Champa so on the way he went and picked up some 1 kg potatoes and then he came back to his house over here he came back to his house over here so where was pandu before where was pandu in initially or before where was pandu before where was pandu before or I can say initially or I can say initially that is basically its initial position that is basically his initial position is that right where is pandu finally where is pandu finally where is pandu either you can say finally finally or I can say currently after some time at this moment where is he he's here so that will be the final position that will be the final position this was the initial position so his position has changed his position has changed that change in the position is called as displacement from where to where where to where is basically called as just displacement and it is just a straight line so displacement is is nothing but where did you go from to the next wear but this wear is initially this where is finally where were you initially where were you finally so if you join a straight line that is going to give you the displacement okay it always joins the initial point to the final point and you will see it is always going to have an arrow Mark that means it will be a vector quantity it will be a vector quantity what will will be the units what will be the units my dear Warriors of displacement what will be the units my dear Warriors of the displacement yes same like position so the SI unit so the SI unit will be none other than meter CGS unit will be ctim obviously you can use feet inches millimeters kilometers also there is no harm in that there is no harm in that keep this in mind now usually whenever I have to use the symbol of displacement the symbol of displacement is s since it's a vector quantity I will put a bar and it is nothing but the change in the position the change in the position and whenever I say change I will use the symbol Delta and I'm talking about position so X position is a vector so I'll put a bar change means Delta understand that change means Delta that is a symbol for that symbol of position is basically X but since it's a vector quantity I'll put a bar over it now remember whenever I say change or Delta means it is final minus initial quantity it's always final minus initial quantity so it's X final minus X initial it's X final minus X initial this is your standard formula for your displacement my dear students standard formula for your displacement my dear students is that clear XF minus XI XF minus XI Delta X Change in the position always Delta means change imagine imagine somebody was carrying some lados earlier earlier there were earlier there were 30 lus now there are only 18 lus so what is the Delta ladu what is the Delta lus my dear Warriors come on quickly answer that what is the Delta lus the change in the lus what will your answer be always change means final minus initial now this is final earlier that is initial so it is always final minus initial so what will be Delta it will be min-2 so the change in the L is - is that clear no it is not + 12 it is minus 12 in this case because final was less than the initial if the final is more obviously it will be plus so change can be positive when it is increasing change can be negative if it is decreasing is that clear everybody with me okay now now if I tell you my dear students if I tell you my dear students example X is X is t² + 4 t - - 3 okay so question is from t isal 0 to T is equal to 2 seconds what is the displacement what is the displacement this is the question equation is given you give me time I will tell you where it is you give me the time I can tell you the position this equation is given remember just like before question is how much did the person displ in 0 to 2 seconds what will you do use the definition of displacement it is nothing but Delta X which is final minus initial final means when X is 2 initial means when x uh sorry when time is two and initial means when time is zero so substitute 2 seconds in this equation substitute 2 seconds in this equation so 2 s + 4 into 2 - 3 that is when I substitute 2 over here minus substitute 0 over here that means when time was 0 what was the position so it will be 0 S + 0 - 3 - 3 + 3 cancels out so this will be nothing but 4 plus if you want I'll just put it over here + 8 - 3 and there will be + 3 over here + 3 over here this - 3 and + 3 will cancel so this will be nothing but 12 M very good very very good everybody with me understood o Clearo yep everyone yes awesomeness awesomeness so this is how you calculate the displacement displacement can be positive displacement can be negative also so I'll put it over here maybe on this slide displacement can be positive negative or even zero can you can you think of an example where displacement is zero my dear Warriors can you think of a uh scenario where displacement is zero so many examples so many examples when displacement is zero one of the example that I can think of you know uh person at rest person at rest yes this is definitely an example there is no movement only so no displacement lot of people say Sir circular motion see circular motion is an example of zero displacement but in two Dimension because you're going in a plane Motion in a plane I'm talking about example in one dimension there are many examples like you go over here and come back over here you go over here and come back over here another example that I can think of you start from a point go over here go over here and then come back over here okay and then you decide no no no I want to be here so this is also zero displacement all these are examples of zero displacement do you understand that but that two in one dimension not even in two Dimension I'm saying in one dimension all these examples are of zero displacement that to in one dimensional motion good morning good morning the you can even catch up at some 2x speed even in the live class you can just rewind back the class and you know catch up if you want to so we have seen what is displacement Now what is distance what is distance distance is the actual path that you take distance is the actual path that you take so over here somewhere I think I put the slide yes this is displacement this is distance distance is nothing but your actual path actual path length path length understand and if you look at it over here it seems to me that distance that distance that the distance because this will be little bit longer than the displacement can I say it is longer than the displacement can I say it is longer than the displacement magnitude is that right or maybe there is something missing or maybe there is something missing I think there is something missing yes distance is more than displacement here but what if what if you started from a point and went only like this went only like this from point A to B in this case the displacement and the distance both will be equal displacement and distance both will be equal you're just going in a straight line without without turning without turning or changing the direction you're not turning or changing the direction then displacement will be equal to distance so that's why more than or equal to this will be the correct state statement this will be the more correct statement do you understand that why have put more than or equal to why have put more than or equal to everybody with me on this very good very good very good excellent now tell me in this particular question in this particular question which of the following are possible or not possible displacement is zero distance is also zero displacement is not zero distance is zero displacement is zero distance is not zero displacement and distance both are non zero which of the following are possible scenario number one scenario number two scenario number three scenario number four more than one options may or may not be correct think about it displacement distance both are zero is this possible in reality definitely a person at rest definitely this is possible if you are at rest you're not moving so no distance and obviously initial and final positions are same distance is zero that means you did not move only there is no path only you have not moved so no length of the path but there is displacement I don't think this is ever ever possible I don't think this is ever ever possible very good who was that janani already answered very good Rupa very very good goam Sia Prasad very nice what about the third one definitely this is possible it's like saying I started here went here and went here and again came back so you are coming back to the same point or I started at this point went there and came back over here so even this one I went here and again I came back like this right so this is also zero displacement and but distance is n here obviously this is is definitely possible many cases are there you start at a point and just go over here yes there is distance and there is displacement so 1 3 and four are possible two is never ever possible two is never ever possible very good also one interesting thing which had been asked in need in different ways look at these graphs look at these graphs tell which of the following may be possible or not possible may be possible or not possible for distance for whom distance this is distance versus time this is distance versus time not displacement distance versus time symbol for distance is d symbol for displacement is s okay check these graphs check these graphs this graph is one like this another graph is like this okay it's flat like this after that another graph is you know like this okay then another graph is like this come on tell me which of the following graphs are possible or not possible this kind of concept also has been asked many times come on my dear Warriors come on my dear Warriors and if you're joining in late smash the like button immediately quickly do not forget to show your immense love and support and if you're watching this recorded I would also love to see your comments because many of the live students are already chatting over here so that way I know that you're at least watching the lectures recorded I know your names too right okay so out of them is this possible definitely uh as time progresses distan is increasing this is definitely possible here I moved moved moved and then I stopped distance is no longer increasing but yeah this is possible so what is showing is I moved initially and then I stopped moving so that is also possible Right very good what about third one and the fourth one I don't think this is ever ever possible you might be like sir why but what is the problem in this what is the problem in this anybody anybody what is the problem once distance goes up how can it decrease distance can only increase it cannot decrease if I travel someplace and if I come back will my total distance traveled increase or decrease obviously it will still increase so you cannot say oh I'm going like far away sir I'm going far away so distance is increasing as I come close then my distance is decreasing no because you're again traveling as and when you travel your distance keeps on keeps on increasing just like in your bike or in your car you might have seen there is a odometer which keeps on increasing because you go to the school and come back does it say oh you went and came back to the same place let me reset to zero no right so irrespective of how you are traveling it keeps on moving ahead increasing so hence it can never ever decrease so that's the reason why this is invalid this thought definitely invalid it is increasing decreasing in fact you are a time traveler here you are going back in time how can you go back in time this is is definitely not possible your time traveling here understood you're going back in time this is not even allowed this is illegal illegal to do such things okay so that was distance and displacement so my dear students have you understood distance and displacement thoroughly till now I think you have learned all the different aspects related to distance position displacement properly I'm pretty sure you have learned a lot of new Concepts till now it's time to move now to Velocity I believe yes let's talk about velocity and speed and how they are related to the displacement clear very good very good Rupa hello Mohamad join in I think you guys are late but it's okay you can catch up at any point of time anyways this is a chapter which you might have done before maybe you might know few things here and there okay so now my dear students over here when we talk about V velocity velocity and speed the only difference is one is Vector one is scalar that's all velocity is how fast are you moving how fast are you moving right and where are you moving to where are you moving moving towards so two things are there two things are there two question questions are there for velocity but when we talk about speed when we talk about speed it's only how fast how fast are you moving that's all so in case of in case of velocity we are talking about magnitude we are talking about magnitude as well as as well as direction as well as Direction but in case of speed you are just talking about the magnitude understand that so that's the reason why velocity becomes a vector quantity because it has both magnitude and Direction whereas speed only requires magnitude so I would say it is a scalar quantity it is a scalar quantity is that right also remember one more thing that these both are measured in the same units these both are measured in the same units what are the units usually it is m/ second or kilomet per hour or I can also use cm/ second you can also use millimet per minute so many units you can make one interesting thing is you should know how to convert from meters to second to kilometers per hour and the standard conversion factor goes like this if you know something if you know a speed in kilomet per hour in Kil per hour then what you do is you multiply it by you multiply it by 5 and divide it by 18 to convert it into m/s to convert it into velocity of m/s understood if some speed is given in km/ hour to convert it into me/ second multiply by 5 by8 to give you an example to give you an example 72 km per hour I want to convert into me/ second so I multiply by 5 and divide it by 18 18 goes with 72 four times it's divisible 18 4 72 so 4 into 5 that's 20 so that is 20 m/s is that clear this is a conversion factor which everybody must be aware of this will come up many many times okay very nice 5 by8 good if you want to do from meters to second to kilometers per hour it will be exactly opposite you'll multiply by 18 and divide by 5 multip by 18 and divide by 5 very nice now now another example of velocity is another examples of velocity and speed uh would be when you ask sir you know I saw this amazing Lamborghini or Ferrari car sir you know the top speed was 350 km/ hour so when we are referring to top speed will that be speed or velocity is that scalar or is it Vector obviously I'm talking about top speed I'm not interested in north east west up down how does it matter Lamborghini Ferrari's stop speed is 350 km/ hour will you ask sir was it in the North or was it in the South you'll be like what are you asking man it is top speed doesn't matter where it is so there direction does not count so it is scalar it is speed but if you're talking about hey I saw an aeroplane and you know it was moving at uh whatever 500 km/ hour as it was landing at this particular airport so I need to tell the direction as well because that airport might be aligned in some way the city might be some place and the Aeroplane will be going in a certain direction only then it will be able to land so there I'm maybe referring to the velocity understood my dear students yes very good yes very good very good awesome awesome let's move on let's move on to the next question okay and the next concept let's move on to the next concept right that is how do I measure this velocity and how do I measure this speed so let's talk about that whenever you want to measure the velocity and that to instantaneous because there are two things two types of velocities or speed one is instant one is average instant means at that moment when you are accelerating on your bike you can see the speedometer keeps changing so that is showing instantaneous speed but obviously when you travel from one place to another there is a traffic signal you stop there is a speed breaker you slow down there is an empty road you speed up there is a curve you again slow down so your speedometer will keep on weying so on an average what was the reading will be the average velocity and you know at any instant means at that exact moment at that exact moment so the meaning of average average velocity average velocity the symbol for that usually is V with triangular brackets V with triangular brackets is nothing but how much is your displacement how much is your displacement divided by the time how much is your displacement divided by time so average velocity will be displacement by the time taken divided by the time which you have taken similarly similarly the value of average average speed average speed I will use the symbol V with like this triangular brackets means average triangular brackets means average there is no need of bar it is always the distance that you have traveled it is always the distance that you have traveled upon the time that you have taken the symbol for distance is D and time that you have taken is T so this is the value of average speed this is the value of average speed speed is Distance by time distance is speed into time time is Distance by speed you have learned this in nth grade same same thing you are learning again over here but these are all average quantities these are all average quantities do you understand triangle means what these triangular brackets mean mean what average it symbolizes average so if I write triangular brackets f it means average force okay average force so anything inside those triangular brackets is average keep these things in mind very good awesome now what is the meaning of instantaneous what is the meaning of instantaneous so when we refer to instantaneous instantaneous velocity instantaneous velocity it is nothing but a very very small displacement at that moment I'm moving a small amount so very very small displacement very very small displacement in a very very small time interval in a very very small time interval now the symbol for displacement is s like I have shown you over here but remember I can also write displacement as Delta X I can also write it as Delta X everybody agrees and time taken T can also be written down as delta T if you want to write it delta T is the change in in the time or a time interval from here to here from 1 second to 3 seconds that's a Time Gap interval so delta T you can also put capital T symbol S change in the position Delta X from initial to final so it is final minus that initial position that is your displacement so when I talk about instantaneous velocity and when you try to compare it with average velocity you will realize average means a long time interval 1 second 5 seconds. 5 Seconds 3 seconds 1 hour 10 hours 5 minutes 20 minutes that is average but when we talk about instantaneous my dear students then it's a small interval and small displacement so my Delta X and delta T no longer are small so when I reduce reduce the time interval this will also reduce when I reduce the denominator this numerator will also reduce because if I'm measuring only for a small time I'm measuring ing only for a small time obviously the displacement will also be very small so this time interval is becoming very small so I will write it as delt T tends to zero often you will see this thing often you will see this thing you will see this thing Delta X by delta T you will see delt T tending towards zero it's the limit of it limiting you might have heard of this word limiting reagent it is a limit of something like everybody has a limit no to tolerate something my patience level exceeded sir enough I got very irritated with my friend so that's why I fought because he crossed his limits he crossed his limits he was insulting me in front of the entire class so same way in mathematics or in physics limits meaning you are almost limiting it to zero making it come very close to zero zero is its limit it's becoming very small but not yet zero because if it is zero time then you cannot move only right so it's very small number coming close to zero in that small time how much did you move but doesn't this look scary doesn't this look scary so we requested the mathematics people that listen we can't scare need students like this by writing limit delta T tends to Z Delta Delta X delta T you know one funny student was like sir can I cancel this Delta and Delta also I'm like yeah why not then you do one thing cancel this also and this also you cancel then you do many more things no you put l i m and this and Delta and this and this you write and then you cancel this also and this also so this will become l i m and like this and like this and zero then you think what is this symbol are these symbols from some wakanda or some tribal area or maybe from some prehistoric era what are the symbols you can think of of that also so guys there is no end to uh stupidity like that so you cannot cancel things like that there are having some meanings they are operators they are operators Delta Delta does not cancel like that right very good so understand my dear students there is a very easy way of writing it and we requested mathematics gentlemen that please I request you to make it look simple and okay fine no problem you just write it as DX by DT DX by DT what is again don't that stupidity sir d d cancel sir X by T no no no no it is D of x d of T it is not D into T it is not D into X don't look at it like that so when I write DX by DT it means very small displacement in that very small time DX by DT is that right everybody understood so DX by DT is nothing but the very small displacement upon very time small time interval that's that's what it is representing in so often it is also called as often it is also called as derivative derivative or differentiation differentiation differentiation differentiation of X of X with with time differentiation or derivative of x with time while saying it you you can say derivative of x with time or you can say it D differentiation of X with time or if you don't want to say derivative of differentiation of you can just say DX by DT DX by DT that is also fine also one more way of writing it is or or you can also say it is rate of change rate of change of X with respect to time rate of change of rate of change of X with respect to time so for example if I put Dadu Dadu by DT what does it mean derivative of ladu with time differentiation of ladu with time rate of change of ladu with time if I put DF by DT F stands for Force rate of change of force with time derivative of force with time differentiation of force with time if I put DV by DX where v stands for velocity rate of change of velocity with respect to X derivative of velocity with respect to X differentiation of velocity with respect to X understood the meaning of the symbols okay it's D of v d of X DD don't cancels it is not multiplication is the small change in velocity small change in position Small Change in force small change in time that is what it means is that clear o perfect o understood o yes that's instantaneous velocity so that's all the definition I mean I should block the entire slide so might as well just put a star Mark over here this is the complete definition of instantaneous velocity instantaneous velocity same thing goes for Speed it will be d uh small distance upon small time so I'm not going to give that again it's the same thing instantaneous speed instantaneous velocity it's the same thing now one thing that you should also know is that one thing that you should also know is that instantaneous velocity instantaneous velocity is just V bar average velocity is like this symbol and when they just say velocity the velocity of the object is 20 km per hour in the north Direction then am I referring to instantaneous or am I referring to average the velocity of the object is 20 km/ in the north direction am I talking about instantaneous or am I talking about average whenever they just use the word velocity they don't tell whether it is instantaneous of average understand it is always instantaneous it is always instantaneous okay or you can just say it's the velocity just using the word velocity means just like instantaneous velocity is that okay SS student just be my student and in the long run you will become I think more smarter than me only don't worry yes very good very good Kudos okay now tell me one thing my dear students is it possible that average velocity and instantaneous velocity are same is it possible average velocity and instantaneous velocity are same are same are same for the motion are same for the motion is that possible are same for the motion is this even possible or not come on think about it and tell me if you think yes let me know with an example if you think no explain why it is not possible explain why it is possible goam I just said I just said ke when I say velocity of a particle is 5 m/ second I'm talking about instantaneous I'm not talking about average if it is average they will tell the average velocity of the particle is blah blah blah okay so when they use the word velocity this just instant instantaneous okay is it possible now average velocity and instantaneous velocity are same average and instantaneous are same is that possible no no think about it it is possible sometimes it is possible sometimes if if if it is moving if it is moving with with constant speed constant speed if it is moving with constant speed without changing the direction without changing without changing direction think about it think about it imagine there is a particle which is going at 20 m/s after some time it is still here and it is it is here and speed is still the same after some more time it is here and the speed is still 20 m/s speed is same direction is same velocity here here here here is same 20 m/ second is 20 m/ second is 20 m/ second is 20 m/ second is so velocity hasn't changed and average velocity is also going to be 20 average velocity is also going to be 20 is that right so is this possible yes only if it is moving with a con Conant speed only if it is moving with a constant speed okay so only then only then it is possible only then it is possible but are there situations where it is not possible are there situations where it is not going to happen yes there are imagine imagine a situation where the speed of the particle is 20 m/ second then it is 5 m/s and then it is let's say you know 0 m/s that means it stopped that means it stopped over here 100% the average velocity is not equal to the instantaneous velocity average velocity is not equal to the instantaneous velocity because instantaneous velocity is not even constant it is not even constant it is continuously changing so understand average may not be equal to sometimes it may be equal to understood everybody all these things are never told in many coaching by many teachers but I am here sitting over here explaining all these things to you because these are all small small things but these need to be told to you only then you realize the real physics you get the feeling of the physics and you will not make conceptual mistakes so till now what did we study till now what did we study average velocity is displacement by time average speed is Distance by time and and these are average values so I will use Delta means change but the moment I go to instantaneous it becomes DD d means very small change it's a also called derivative or just a rate of change and you can use derivatives for many things in life in certain situations when the speed is same and direction is not changing average values and instantaneous values are same but obviously if I'm accelerating decelerating increasing speed increasing speed changing direction gone velocity only will keep changing so obviously average won't be equal to instantaneous is that making sense and whenever I refer to the word velocity I am referring to instantaneous if I want to tell you average velocity I will mention the word the average velocity of the particle is so and so m/ second understand that all these are important things all these are important things things okay so we have done this we have done this also okay now now imagine I ask you to give me an example if average velocity is zero but average speed is not zero is this possible is this possible I and if it is possible think of an example average velocity is zero but average speed is not yes yes you might have a test I guess I think it is possible average velocity zero means what your displacement should be zero definitely it is possible and average speed is not zero means distance traveled distance traveled is not zero oh this is definitely possible that means you start at a point go over here and you come back you start at a point go over here and you basically come back so in this case displacement is zero but uh distance is not zero so definitely this is possible definitely this is possible no don't give circular motion circular motion is an example of 2D if you give example of circular motion you'll get minus one marks in neat in imagine there is a statement which says in one dimensional motion is it possible average velocity zero and average average speed is not zero um statement is there assertion reason is there or statement one and statement two is there and statement two says yes in circular motion something like that then you'll be like huh in circular motion displacement is zero but in the main statement it said Motion in 1D Motion in 1D and circular motion are not the same thing they are circular motion is motion in a plane so then circular motion will not be an example okay so this will be an example you go front and you come back so this is zero displacement and no distance and some distance okay so I hope till this point everything is clear I hope till this point everything is clear let's also look at the graphs let's also look at the graphs and also let's look at uh some more things like average and instantaneous in these uh quantities whenever you are looking at average of any quantity you will take a interval sometime Gap interval Delta but when you're looking at instantaneous it's a small change so remember one thing if you're looking at average quantity if you are looking at average quantity of anything average quantity of anything there will be some points between which you want to measure the average let's say these are those two points let's say these are those two points maybe this is the x-axis maybe this is the Y AIS maybe this is the x-axis maybe this is the y- axis from here to here I want to measure the average so from here to here there might be some Delta X I will use different symbols please let's not use these things because changed the axis names so from here to here this would be Delta X this would be Delta X I'm changing changing the x-axis by some value how much did my y value change by my y value my y value was here then it went till here so clearly there is a change in the Y value there is a change in the Y value so that change in the Y upon change in the x is the average quantity average rate of change average rate of change is Delta y by Delta X Delta y by Delta X also one interesting thing to note if you can form a nice right angle triangle over here if you can form a nice right angle triangle I hope you can see there is a beautiful right angle triangle which which can be formed over here then you can just join these two points you can just join these two points measure this angle it will be Theta measure this angle it will be Theta this will also be tan of theta this will be also tan of theta so if you make a triangle then if you join a line between those two points then tan of that angle made by the horizontal is also the average rate of change is also the average rate of change whereas in instantaneous will you have two different points no right you will have the same point or it is very very small they are almost touching each other visualize this these two points come very close this dotted line that I have drawn this dotted line that I have drawn will almost be at that point only this triangle will become very very small over here this triang Le will become very very small over here right and then when I draw a tangent that's when that's when I can actually measure the rate of change when I draw a tangent the tangent might make some angle with the horizontal so this is the tangent which is drawn this is a tangent which is drawn at that point add this particular position at this particular position I want to know what is the rate of change so this is the instantaneous instantaneous rate of change instantaneous rate of change so let's say if if this one is your x-axis this one is your y AIS then instantaneous rate of change will be represented by Dy by DX Dy by DX rate of change of Y with respect to X and that will be tan of theta again but this Theta is the angle made by the tangent with the horizontal line angle made by the tangent with the horizontal line that will give you the instantaneous value is that very very clear yes doctor said you can attend it at any time but if you want all India ranking then you need to give it in that specific window only otherwise it will not work cool cool so let me give you some examples on that as well one second let me give you some examples on this as well say I have a graph and this is position this is time and the graph goes like this and the graph goes like this okay I have drawn one graph let's see if you guys can answer some questions based on this graph tell me Tell tell me at T is equal to 0 at T is equal to 0 what is the velocity in when I say velocity it means at that moment at that instant come on quickly answer in the chat box I want everybody to answer it after this this knowledge of graphs and basically slopes and derivatives will be very very clear come on think about it and tell me at time is zero this is position this is time I want to know the velocity what did I tell you velocity velocity is nothing but velocity is nothing but DX by DT rate of change of that quantity with the time DX by DT I told you that is instantaneous velocity and whenever you are looking at instantaneous you should look at the tangent and you should measure the tan of tangent tan tangent forget the tan sorry forget the Gent you will see tan of theta Theta is the angle made by the tangent that's all you need to see so if you draw a tangent so if you draw a tangent at the origin how is the tangent going to be I think the tangent is just going to be horizontal like this the tangent is just going to be horizontal like this very good if it is horizontal what is the angle made the angle made is zero so V will be tan of 0 which is 0 m/s it has no velocity only very good no it is not square root of 3 it is zero only if you see at this point not here at this point the tangent drawn is parallel to the horizontal line so it is making 0° angle so tan 0 is 0 that's all okay let's see if you guys can answer this at T is equal to 2 seconds what is the velocity at T is equal to 2 seconds what is the velocity quickly think and tell me at 2 seconds at this point you will draw a tangent you will draw a tangent see this tangent what is the angle which it is making with the horizontal line it is making 60° so what will be the velocity at that point it will be tan of 60 tan 60 means < tk3 which is 1.73 m/s 1. 732 is the value of root of three so that's why that is the answer very good very good very good Square ot3 excellente similarly if I ask you at T is = 6 seconds what is the value of velocity what is the value of velocity quickly think and tell me at T is equal to 6 seconds think carefully and answer think carefully and answer what is the velocity at that particular point at 6 seconds you can see the tangent drawn the tangent drawn is this one this is the tangent drawn and it is making 40 5° with the horizontal so many people might say sir it is tan 45 but that is not correct actually it is not going up it is coming down so the angle made if you think carefully is towards the down side it is minus 45 so actually it will be minus of tan 45 it will be negative many people have wrote the answer as one that is not the correct answer it is negative because it is going down tan 45 is 1 so - 1 m m/ second will be correct if you don't put minus1 if you put answer as one then you will get minus one by the examiner understood you'll get Negative marks so be careful you have to see how it is going it is going down this is going up it is increasing so if you see over here if you see over here the angle was this way if you see over here the angle was technically down the angle was technically down so that's the reason why it is negative so this is positive angle this is negative angle keep this in mind got it very good now if I ask you when when is velocity zero when means Time come on think and answer this question when do you think the velocity is zero looking at this graph when do you think the velocity is zero looking at this graph one answer I already know the time tangent drawn here is parallel to the horizontal line so it is at t equal to 0 seconds t equal to 0 seconds definitely is there any other point where the tangent drawn is hor horizontal where the tangent drawn is horizontal yes I think so at 4 seconds at 4 seconds if you notice the tangent drawn is horizontal is that right everyone exactly so hence can I also say it is also so at 4 seconds and no other point I can see the tangent drawn is horizontal so these are the only two time instance these are the only two time instants cool clear perfect okay then if I ask you when when is velocity positive or negative when is velocity positive or negative when I say Vel velocity is positive that means the tangent drawn makes a positive angle I can see right after 0 seconds any tangent that you draw till here is going up only till 4 seconds just before 4 just after zero tangents drawn are always pointing upwards is that right so can I say all the positivity or it is positive from 0 to 4 seconds 0 to 4 seconds from 0 to 4 seconds and where is it negative that means it should be pointing downwards right after 4 seconds it is pointing down even here don't say it is positive no it is still pointing down only whatever tangents you draw it's always pointing downwards so hence the answer will be negative will be for 4 seconds to 8 seconds 4 seconds to 8 Seconds understood how to solve these questions are you getting confidence now very good why 4 seconds for the previous one because at 4 seconds do you see the tangent drawn is parallel it's parallel so angle made is 0° with the horizontal line so that's the reason why tan 0 will be zero so that's why at 4 seconds also the velocity was Zero velocity was Zero is that okay tangent yes these are all numerical questions graph based questions which can come in the exam there also numerical only okay so let's do this coordinates is given by this what is the average velocity from 0 to 4 seconds what is the average velocity from 0 to 4 Seconds come on think about it average velocity from 0 to 4 seconds whenever question comes on average velocity you have to find the displacement by time that means Delta X X by the time interval now the Delta X will be final position minus initial position upon that time interval now observe carefully X4 means in this value in this function substitute time as 4 so that will become that will become 7 into 4 - 3 into 4² minus x0 means substitute 0 over here so that is become 0 - 0 only and how much time are you traveling from 0 to 4 what's the time interval it is obviously 4 seconds so this will become 7 4 are 28 and 4 square is 16 16 3 is are 48 0 - 0 0 nothing will happen divided by 4 so this will become 28 - 48 that's - 20 by 4 which is - 5 but that will be m/s so - 5 is there as option b b for biology how many of you wrote B for biology around there very good s Prasad excellent Mali yes sjay the answer is option two yes satatus 5 m/s Perfecto Perfecto Perfecto moving on to the next question oh I think the next question will now start after acceleration let's go to acceleration now ready for acceleration let's accelerate guys okay now there are some misconcepts in acceleration let me clear that first see all these printed slides you are going to get but I feel you are more always interested in this written slides or whenever I explain by my hand right cool B for ID Bombay diwakar yes so what are your targets guys because uh often uh you know I ask my J students what are their targets and most of the times they till it Bombay it Chennai ISC or triple it and other things and uh and I ask you guys I think usually you tell as or afmc is that your target to is that your dream to afmc and aims or is there some other thing that you want to do because sometimes you know some students have another passions also like okay I want to write need but I want to do this some very special thing or I don't know you want to do something abroad or maybe you want to uh go to a specific government Medical College am baswaraj sir Ames wow nice nice masaj are is aiming for ases and he's going to write neat exam too how was J paper J paper was very Lalu I don't know S sansi I think you should always have a Target I feel Sarat has already put some hearts over there Ames man mangalagiri oh okay I don't know where that place is though Target is good doctor I love that answer SAA Prasad that's a very very nice answer that you gave 150 good marks in yesterday shift paper 150 is okay marks not great but considering you just give physics and chemistry then it is okay otherwise no okay so yeah that's that should be the always the aim I like the answer what you guys gave um always being a good doctor is the most important thing my dear students uh a is just one Milestone IM is or afmc or government Medical College or whatever College you are aiming at that is just one uh path I would say that is not the destination at the end of the day the destination is to become a doctor and you can become a doctor bya many ways and to become a good doctor is the most important thing right so I really hope that this channel produces the best and the finest uh you know doctors in the country and one day when you look back and you see Juniors over here you will feel very proud that these students also are studying just like like you did once upon a time and you would probably then see this channel would have gone to really great Heights maybe a million subscribers too so make sure you're talking about this channel make sure you feel for this channel make sure you grow this channel just like a family because we are all family members out here right and we are your guiding forces so make sure you are one of those mascots you are one of those people who always markets this channel thank you so much let's talk about Accel now let's talk about acceleration now acceleration acceleration see if you are walking with constant speed then you are not changing your speed then you are not changing your speed right but when your speed is changing then I can say you are accelerating when your speed is changing now your you are moving slow then you move fast then you move even faster then you are accelerating or you are moving you slow down slow down slow down speed is changing then also you're set to accelerate basically you're set to accelerate Whenever there is change in speed but how quickly you change that speed matters and that decides the acceleration so acceleration is also called as the rate of change rate of change of of velocity how quickly basically how quick you are or how quickly velocity is changed how quickly a velocity is changed let me give you an example from this you can tell me who has more or less acceleration imagine a particle going at 10 m/s and it increases the speed to 30 m/s and this is at t equal to 0 this is at t equal 2 another example another example where a particle was going at 20 m/s and it changed its speed to 40 m/s this is at T is equal to 0 this is at T is equal to 4 seconds tell me in this case if the acceleration was A1 in this case the acceleration was A2 tell me where was the acceleration more or was it less more or less equal in this case or in this case in this case or in this case if you look at the definition it says how quickly the velocity changes in that particular time so over here from 10 you have gone to 30 from 10 you have gone to 30 so how much was the change how much was the change my dear students from 10 you went to 30 so change is final minus initial so isn't it plus 20 m/s that is the change of velocity is that right over here from 20 you went to 40 so 40 - 20 is again 20 so the change was 20 m/s yes or no my dear Warriors here how much time did you take you just took 2 seconds here how much time did you take you took 4 seconds so isn't this quicker because isn't this quicker because there was less time here here there was more time so this was much slower acceleration the same change occurred the same change occurred faster here it occurred slower so my dear Warriors isn't A2 going to be less than A1 isn't A2 the second case acceleration going to be less this is going to be little bit more very good understood Clearo how this works acceleration right so there are again two kinds of acceleration one is your average Accel acceleration and one is your instantaneous acceleration so when we talk about average acceleration average acceleration we are referring to how much is your change in velocity how much is your change in velocity upon how much is the time taken to change that velocity how much is the time taken to change that velocity so average acceleration change in velocity means Delta V upon delta T you can also write Delta v as V final minus V initial upon that time interval uh just like before remember the unit the unit of acceleration okay because this is meter per second this is second so it will just become m/s square or cm/ second square or kilomet per hour Square those will be the units of acceleration if you talk about being V vector or scalar well whatever is the arrow Mark here will be the arrow Mark here so they are vectors so the direction of the change of the Velocity is the direction of acceleration strictly speaking so it is also a vector quantity it's a vector quantity in the direction of the change in the direction of the change of your velocity so that's how acceleration is okay keep all these things in mind in fact I can block the entire thing so I'm just putting a star Mark here so that you know you have to know all these things over here this is the definition of average acceleration cool now what about instantaneous acceleration what about instantaneous instantaneous acceleration sometimes just called as acceleration if I just mentioned the word acceleration that is also the same thing so that will be you take a very very small time you take a very very small time and in that small time what is the small change what is that small change in the velocity that is your at that moment acceleration so the value of the instantaneous acceleration is the small change in velocity upon the time time but this time should become very small it should limit to very very close to zero very very close to zero but what will we request the mathematicians please listen to me I don't want all these complex numbers limit delta T TS to Z Delta V delta T it looks very very tedious I don't like it you give me a shortcut way of writing it so the mathematician said okay no problems you can just write it as DV d v by DT you can just write it as DV by DT that's one and the same thing that's one and the same thing as writing this do not cancel D and D obviously don't be that naive now okay we cannot cancel that D and D we have seen that it is not D into V it is D of v d of V means Small Change in V it's not D into T it is D of t means a small change of time that is what it is referring to and just like before I can call it as the derivative derivative or differentiation differentiation of velocity with respect to with respect to time with respect to time you can also call it rate of change of rate of change rate of change of V with time one and the same thing whatever comes on the top is the rate of that with with respect to whatever comes below that's how it is so now tell me my dear students we have put all these things as before okay we have put all these things as before tell me my dear students over here if I again draw a graph of velocity versus time velocity versus time and let's say that graph is something like this and maybe this is 1 second maybe this is 3 second at 1 second maybe your velocity was 2 m/ second and maybe at 3 second maybe your velocity was 8 m/s from this graph can you find average or instantaneous value of acceleration I think you can only find average because it's over a period of time it's an interval of time it's not at the moment so whenever such graphs are seen you will be more interested in the average or what you will be finding is the average value so if the question says what is the average acceleration from from 1 to 3 seconds from 1 to 3 seconds that's the question that's the question what will you do use the definition of average acceleration average acceleration is change of the Velocity upon the time change of the Velocity upon the time Gap if you notice carefully you will realize this is the time Gap this is the time Gap also from or in this time Gap my velocity Has Changed by this much so this is the change in the velocity so can you quickly tell me what is delt T delt is 3 - 1 3 - 1 that means 2 seconds can you quickly think and tell me what is Delta V Delta V is nothing but 8 - 2 which is 6 m/s so won't this be 6 m/s upon 2 seconds which is 3 m/s Square so the average acceleration is 3 m/s Square understood o clear oh how this works everybody with me okay you should be very very convergent fluid you should be skilled in reading and analyzing the graphs because these questions are very common imagine a question says like this a question say is like this this is velocity this is time and the question is somewhat like that and maybe at 3 seconds or maybe at 2 seconds they have just drawn a tangent over here they just drawn a tangent over here and the angle given over here is 30° the angle given over here is 30° and then they ask you what is the acceleration what is the acceleration at T equal to 2 seconds what is the acceleration at T is equal to 2 seconds then you will think okay acceleration is asked that means it is instantaneous acceleration instantaneous means DV by DT what did I tell you about DV by DT it is rate of change and whenever it is rate of change of any y AIS quantity with the x-axis quantity with the with the x-axis quantity I am referring to the tangent or the tan of the angle made by the tangent with the x-axis right so we all can see that this is the tangent this is basically the tangent so therefore I should take just the tan of the angle made by the tangent with the horizontal line tan 30 is 1 byun3 so 1 byun3 m/ second Square understood Clearo how this works yes Gotham we will be completing this chapter this is how the solution will come okay this is how you find the instantaneous acceleration okay so I have spoken about we have started with what is acceleration uh right it is the rate of change of velocity how quickly you change the velocity right we have seen what is the formula for average value which is big change in velocity upon big time interval units vector quantity all these things we have seen also we have talked about instantaneous value which is rate of change of something which is the rate of change of velocity and I have showed you examples related to that now in your ncrt you might have also seen this uniform and non-uniform motion this is a very important difference table sometimes questions can be directly asked in your boards but also obviously important from the need perspective uniform versus non-uniform uniform motion means the body is moving straight line with a steady speed like this with a steady speed nonuniform motion means the object is moving on a straight line with variable speed so here steady speed is there whereas over here what is there over your variable speed is there so sometimes you moving slow sometimes you are moving fast so speed are changing here in uniform motion it covers equal distances in equal time it covers if I move 1 m in 1 second next 1 second also I'll move 1 M if in 1 second I'm moving 10 m next 1 second also I'll move 10 m obviously in non-uniform motion you will move unequal distances in that same time maybe in the first second I move 2 m next second I'll move 10 m next next second I will not move only next second again I'm moving 3 m so it is unequal distance it is similar to the actual speed of the object this part we have seen the average and the instantaneous value will be same average and the instantaneous value will be same so there is no point of talking about average or instantaneous separately when the motion is uniform every instant the speed is the same m/s here it is going to be different every time the speed is going to be different right so understand that distance time graph will show a straight line makes sense if you are going uniformly every time I'm moving some distance every time I'm moving some distance every time I'm moving the same distance so the graph will be a straight line whereas here the graph won't be a straight line here the graph shows a curved line understand that as compared to a straight line is that clear my dear Warriors it will be a curved line because every instant you're moving different different amounts so that's why it is a curved line because you are going with constant speed because you're going with constant speed meaning are you changing the velocity are you changing the speed no right so what will happen you will have zero acceleration no acceleration at all but obviously over here sometimes you are moving fast sometimes you're moving slow fast slow so there are changes in the velocity sometimes it increases sometimes it decreases so that is why it is nonzero acceleration that is why it is nonzero acceleration I hope this is clear he why did I draw tangent in the previous question because the question was an acceleration or instantaneous value do you remember just some time back I just showed it right over here maybe uh join in late or something where did it go here whenever you want to find in instantaneous or rate of change you draw the tangent whenever average value is asked for the rate of change then you take two points measure the height measure the base and that's how you divide these quantities and get the average value when it is instantaneous it is derivative or rate of change you draw the tangent measure the angle which the tangent makes with the horizontal that's how you do it that's the reason why we have shown the tangent in this case okay that's the reason why we have taken the tangent in this case whereas when it is average value when it is average value then I know don't need the tangent just take two values here two values here find the difference here difference here and you can just divide them is that clear everybody okay shall we move ahead now to the next part now if you want I will take a separate lecture on calculus but let's just take these things for granted don't ask me sir what is how does it come and all that now let's not worry about it just remember few things whatever I'm going to tell you now whenever whenever you are differentiating taking derivative of T ra to n t ra to n then the answer will be n into T ra to nus1 example example the derivative of T Cube derivative of T Cube here n is 3 so the derivative or the rate of change will be put that n put that n outside that means three will be outside reduce the power of time by one so it will be T to 2 another example let's say d of let's say t 7 ided DT the answer for this will be nothing but put that number seven outside it will be t 2 7 - 1 is 6 another example another example derivative of t with respect to T in this case just look at it this way it is d t to 1 by DT put that one outside and T's power reduce it by 1 so 1 - 1 T to 1 - 1 so that is nothing but T to 0 which is just simply put one anyways DT was going to get canceled with DT completely so 1 is to one or just one that is how you get it okay similarly if I had D of root t with respect to T okay just by hard this formula for now don't worry about other things if you know derivatives good if you don't know also it doesn't matter if you just know this formula it's more than enough you don't have to go deep into derivatives you are not studying mathematics over here then the power of time then the power of time whenever there is root then it is having a power of half so take that half outside take that half outside reduce the power of time by 1 half - 1 so that will be half into T -2 which is 1 by 2 T2 which is as good as saying 1 by 2 < TK T 1X 2 root T you can just write it like that is that okay everyone everyone with me till this point is it clear till this point is it clear my dear Warriors okay then we'll go ahead this is one of the formulas this is one of the formulas which you should know this is one of the formulas which you should know another formula which you should know is derivative of a constant derivative of a constant is always going to be zero derivative of a constant is always going to be zero best example derivative of five with respect to time will be zero it's just a constant so don't matter doesn't matter just make it as zero another thing which you should know about derivatives is if you have two things added or subtracted we'll just take the simple rules for now I'm not giving all the rules because I'm just interested in the application of it let's say you have uh some function here and another function here and you are adding it or subtracting it you can take the derivative separately you can take the derivative separately and then add or subtract it example if I want to find the derivative of T CU + T 4 take the derivative separately so derivative of T Cub separately derivative of T 4 separately and then you add it here now use x to n formula so n is 3 reduce the power of time by 1 so it will be T to 2 4 comes outside reduce the power of T by 1 so it will be T Cub if there is minus here there will be minus here also this is how this works this is basic derivatives which you should know mainly you should know this formula right now I'm just teaching you the basic applications if you want we'll have a detailed session only on derivatives and integration just these few things you know because we just learning how to use them the exact reverse of this is integration the exact reverse of this is integration and the symbol for that is this so if it is T ra to n DT T to n DT this is integration this is integration this is integration I'm just reminding you of that integration we'll have a separate class if needed then the answer will be here you put T to n + 1 upon n + 1 and you put a constant of integration and this C is nothing but also called as the constant of integration constant of integration also just integral DT is just t + C just integral of DT is just t + C just to give you certain examples over here just to give you some examples over here integral of x Cub DX just like this X Cub DX here that 3 is that n so it will be X ra to 3 + 1 n + 1 that means 3 + 1 by 3 + 1 + C so it will be x 4 by 4 + C another example integration of integration of T DT integration of T DT this is as good as saying integration of T to 1 DT T's power is 1 so so increase the power of T by 1 instead of decreasing when in derivatives decrease in integration you increase upon 1 + 1 + C so this will be T to 2 by 2 + C keep these things in mind these are standard basic things everyone okay very nice in integration only remember in integration only you can find something called as area under the Curve area under the curve meaning meaning if you have some Y versus X graph something like this and there are two values of X there are two values of X some random two places random two places two values of x from this value to that value what is the area under this graph what is the area under this graph is given by is given by integration of that function integration of this y value with respect to this x value from X1 to X2 this is also called as definite integration this is also called as definite integration this is also called as definite integration this is with some Val Val on the top and Below not like before there were no values these were actually indefinite indefinite indefinite integration whenever you have indefinite integration you will have some constant which is coming whereas in definite integration you will never have constant of integration I will give you an example then you will understand it imagine somebody tells you integrate just integrate x to 2 DX or let's just take T 2 DT from 1 to 2 from 1 to two that is what somebody tells you what you will do is first don't even look at these numbers at the top and at the bottom what are these numbers by the way called as this number is often called as the upper limit this is called as the upper limit and this this number over here is just called as the lower limit this is just called as the lower limit what you do is just like you normally integrate you integrate what is T to 2's integration use this formula T 2 is integration just use this formula t n + 1 upon n + 1 so it will be T 2 + 1 upon 2 + 1 don't put constant this is with the limits when Whenever there are limits never ever put never ever put constant of integration constant will come only in indefinite indefinite there is no constant of integration and just I'll put these square brackets put one over here two over here we'll see what to do now T to 2 + 1 is T to 3 2 + 1 is 3 still put those square brackets 1 and two now what you should do is put the of two here and then put the value of one over here and then subtract them put the value of two here that means it will become 2 Cub by 3 then put the value of 1 here so it will become 1 Cub by 3 and then subtract them that's all so this will become 8X 3 - 1X 3 which is 7x3 that's all that's how you do this understood clear let's take one more example so that you guys have an clear-cut idea of this example integration of tdt tdt from 0 to 4 from 0 to 4 what will you do just like you normally integrate you integrate without taking care of the limits as of now don't worry about these numbers this is as good as saying T to 1 so it will be T to 1 + 1 upon 1 + 1 now put square brackets put lower limit and upper limit that's all this will be T 2 by 2 lower limit is zero upper limit is 4 what you should do now put the value of four here so it will be 4 S by 2 then put the value of 0 here so 0 S by 2 then just subtract them so 4 square is 16 and this is 0 so the answer will be 8 16 by 2 is 8 got it everyone so this is basically your standard integration which you should be little bit aware of okay we'll solve some questions then you will understand it now what you should keep in mind is this particular memory chart you have position you have velocity you have acceleration whenever you differentiate position whenever you find DX by DT you get velocity velocity is DX by DT yes or no similarly when you go from velocity to acceleration what are you doing you are just taking derivative of velocity with respect to time you are just taking derivative of velocity with respect to time here it's all about rate of change rate of change rate of change of X with respect to time this was rate of change of V with respect to time it's all about tangents it's all about tangents here on this side it's all about tangents and their tan Theta when you go from position to Velocity or when you go from velocity to acceleration some of the best examples would be like say for example if x is given to you as T Cube if x is given to you as T Cube and somebody asks you find the velocity find the acceleration if they ask you find the velocity find the acceleration what will you do is look at this graph velocity is the derivative of x velocity is nothing but derivative of x with the time just look at that what is X x is nothing but T CU X is nothing but T Cube okay is there some formula which I know yes X ra to n formula T ra to n formula so what will happen that n comes outside the power of time reduces by one so 3 t² is the answer for velocity so therefore velocity is 3 * t² if you know position you can immediately find velocity is that right now in order to find the acceleration in order to find the acceleration you just have to take DV by DT you just have to take DV by DT my dear Warriors now what is v v is nothing but V is nothing but 3 t² V is nothing but 3 T Square 3 is a constant just don't worry about it just bring it outside just bring it outside now just think l logically what is the derivative of T to 2 it's like T to n where n is 2 so 2 comes outside and T to 1 T to 1 which will make it which will make it 6t which will make it 60 so we have found out acceleration so this is how from position you find velocity or from velocity you find acceleration using the knowledge of using the knowledge of derivatives got it everyone right if you go reverse if you go reverse then it is integration if you go from here to here if you go from here to here then you have to integrate so what you get is Delta X is integration of velocity with time Delta X Change in the position is integration of velocity with respect to time so from T1 to T2 like lower limmit upper limit if you go from here to here if you go from here to here from acceleration to Velocity then you get Delta V is integration of acceleration with time lower limit and upper limit lower limit and upper limit this whenever integration comes whenever integration comes with limits basically definite integration basically definite integration you're always referring to the area you're always referring to the area under the graph so here also this is technically area under it is area under velocity and time here it is nothing but area under area under acceleration and time this is area under acceleration time gives me change of the Velocity area under velocity and time gives me the change in the position gives me the change in the position keep these things in mind let's take a example on that twoo it's not that difficult let's understand this example example imagine it is given to you imagine it is given to you all right uh velocity is t² find the displac ment or basically Delta X in first 2 seconds find the displacement in the first two seconds that's what the question says now displacement Delta X is one and the same thing displacement or Delta X is one and the same thing and just now we saw that whenever you want to find Delta X from velocity you integrate so why not write this as integration of velocity with time from some time to some another time but wait a minute I already know the velocity it is nothing but T Square okay okay the velocity value is already given as p² what will these numbers be look at the question first 2 seconds first 2 seconds means from 0 seconds to 2s seconds from 0 seconds to 2 seconds is that right hence this will go from 0 to 2 this will go from 0 to two this is lower limit this is upper limit okay now you just integrate it normally like you do normal integration T to n formula so T to 2 + 1 upon 2 + 1 do not put constants of integration put this number 0 and two over here 0 and two as it is this will become t P to 3 divided 3 and this will become 0 and 2 this will become 0 and 2 now put two over here this will become 2 Cube then put 0 over here this will become 0 Cube and then subtract the two so what will this become 8 by3 what will be the answer me 8 by3 m very good very good j s Prasad awesome you can get the syllabus of the victory test series by scanning the QR code which I just uh shared it's also there on the telegram group and you know before this also I had shared it you can just scan that the start of the session only I had shown okay understood how integration Works to find that displacement you can also check these kind of questions you can also check these kind of questions where it might be given to you something like this is velocity this is time this is velocity this is time and the graph might go like this and then like this maybe this is given as 2 seconds maybe this is given as 6 seconds maybe this is given as 10 m/s and the question could be find the displacement find the displacement in the first 6 seconds find a displacement in the first 6 seconds that's the question now displacement displacement is asked meaning Del Delta X is asked if you go back to this mind map or this memory chart which I had given Delta X can be found by integration which we just did in this problem or it's also area under the velocity time graph area under velocity time is Delta X okay and here this is velocity and time so if by chance I happen to find this area won't that exactly be this which is area under area under velocity versus time perfect so I just have to find the area of the triangle which is half into base which is 6 into height which is 10 area of a triangle is half base into height so 6 by 2 is 3 so this will be 30 m this will be 30 m got it hello Anna good afternoon I must say yes awesome this is how you find displacement so I hope this part is little bit clear now we'll have a separate class if you want on derivatives integration that's the mathematical part I don't want to go too much into mathematics in today's class I'm just assuming you know the derivatives and the integration part although I taught you some bits of derivatives and integration here which is basic application that is okay but main thing is you should know how to go from X to v v to a a to V or V to X this part is integration this part is derivatives for derivatives it is always rate of change remember that whenever it is talking about derivatives it is a rate of change use these formulas the basic formulas which are given when you want to go reverse integration then use these formulas but if there are no numbers on the top and the bottom there is always one con Conant which will come that is indefinite but whenever you see some numbers here then the limits are there it is a definite integration so you just do the normal integration as it is but in the end substitute these upper and the lower limits and then subtract the two that's how you get the value of this this always refers to the area under the graph whenever you put limits there will always be area whenever you take derivative it is always tangents tan angle tangent tan angle basically the slope yep okay I hope this is fine let's do some questions guys coming up on the screen there are some questions on graphs and other things position is given by this T is measured in seconds what is the velocity at this and this what is the average velocity between this and this let me just create a duplicate if I might need more space let's do the first part of the question what is the velocity at T is equal to 0 and T is equal to 2 seconds but what is given to me is X as a function of time from X can I find V from X which is a + BT s can I find velocity yes don't just divide by time this is some equation so you have to take derivative DX by DT so it is basically d by DT of a + b t² so this is addition so I can separate them out I can separate them out I can just put that b outside the D t² over here now it looks simple to me d a by DT a is a number it's a constant so obviously the derivative will be zero here B value is given where is it 2.5 into T s's derivative that number two will come outside reduce the power of T by 1 so T to 1 2.5 into 2 is basically 5T so velocity is 5T so you tell me the time I can tell you the velocity what are the times 0 and 2 so V 0 will be 5 into 0 so it will be 0 m/s this is ncrt question direct this is the first answer this is the first answer everybody second answer velocity at 2 seconds so put 5 into time as put it as 2 so this will be 10 m/s so that is velocity number two as simple as that is that right everybody very good very good but that's not the only question the question is what is the average velocity from 2: 4 what is the average velocity from 2: 4 recollect the definition of average velocity recollect the definition of average velocity it was displacement by time which is Delta X by delta T so I need the change I don't need derivatives anymore so from 2 to 4 what is the interval 4 - 2 4 - 2 and when I'm talking about Delta X I'm talking about position at 4 seconds and position at 2 seconds and then I'm subtracting the two so put the value of four here put the value of two here and subtract the two so it will be a + b into 4 S right that is the first term minus a + b into 2 s that is what you will get a and a will cancel B will be common 4 Square 4 S - 2 s will be there 4 - 2 is 2 B value is 2.5 so I'm just going to put 2.5 at as it is this is 2 4 square is 16 2 square is 4 16 - 4 is basically 12 so 12 and 6 6 into 2.5 my dear students that is going to be 15 m/s just check this out how many of you got it 15 m/ second everybody with me come on my dear students start answering the questions quickly start answering the questions quickly very good yes easy question very good so this is how you do these questions from ncrt let's do more questions which are going to come up yes all the answers matched two cars this was neat 2016 question have positions given by a t + BT Square ft minus t square at what time do they have the same velocity at what time do they have the same velocity so if their velocities are same that means VP must be equal to VQ but positions are given positions are given okay no problem so derivative of the positions derivative of the positions must be equal now we can find the derivative so I'm just asking you derivative of the position of P particle that means a t + BT s and also find the derivative of Ft minus t² so here I can see plus term I can separate them out constants I can bring outside the derivative so a into DT by DT + B into t² sorry not t² d t² by DT will be equal to F I can bring it out so F into DT by DT minus is there so derivative of t² with respect to time this is what it is is that right right everybody till this point clear okay so let's see what is it coming out to be what is it coming out to be a into DT by DT is 1 only nothing there b into T s's derivative T s's derivative will be 2 into T to 1 2 comes outside T's power reduce it by 1 F into DT by DT is 1 only so it will be just F minus t squ derivative two comes outside T to 1 okay bring that 2T over there so it will become B into 2T + 2T = f - A so over here I can just take uh 2T outside and I will have b + 1 over here is equal to f - A so T will be f - A upon 2 uh b + 1 2 b + 1 that should be the final answer f- a upon 2 b + 1 F minus a upon 2 b + 1 that's option number four option number four D for am Delhi very good s Prasad yep awesome if you want I will share the QR code again gaming with no noobs YT I will definitely share it at the start of the lecture initially I had shown the QR code over here so you can rewind back you can pause the video you can scan it through a mobile or I'll share it on the telegram Channel also don't worry about it okay cool that's this question let's move on to the next one coming up on your screen a particle is going along a straight line with this velocity find the average speed that is the question question says find the average speed in this time these kind of questions are very very common in neat these kind of questions are very very common in neat how do you solve it well velocity is a function of time and average speed is asked so what we'll do is first go by the definition average aage velocity or average speed will be nothing but the displacement by the total time displacement is not given but I know displacement is Delta X so how what was the formula of Delta X if velocity was given I remember if I know velocity and I want to find Delta X I'm going reverse I have to go integration way I have to integrate it so actually Delta X is integral of V DT into integral of V DT from T1 to T2 and this t comes over here oh so that was the value of deltax and do I know velocity yes I do know velocity the velocity value is Alpha TQ Alpha T Cub okay what will be the limits of integration what will be the limits of integration from 0 to T from here to here from this point to that point area limits all these numbers will come at bottom and at the top of the integral symbol that's it so now rest is straightforward you just can integrate it take that Alpha outside it doesn't matter take that Alpha outside even that t will come below over here it is just integral of 0 to t t Cub DT 0 to t t Cub DT so Alpha YT as it is T to n's integration formula was T to 3 + 1 which is 4 upon T upon n + 1 which is 4 again put the limits 0 and T as it is put the limits 0 and T as it is so this will become Alpha by T into here put the value of T first so it will become T 4 by 4 minus then put the value of 0 here 0 4 by 4 so 0 by anything is zero so it will just be Alpha by T into T 4 by 4 1 T will cancel so it will become Alpha T Cub by 4 Alpha T Cub by 4 is option number d alpha T Cub by 4 is option number D is that clear D for as Delhi very very good proud of all of you awesome as you see me solve problems I think you are gaining confidence initially derivatives integration application might look scary if it takes some time give it that time you cannot just hasten up that process and say that sir I saw one lecture in that uh you know it was done in 10 minutes or half an hour no you cannot do that it takes days to complete and get that confidence by yourself you have to see the lecture which is slow which is steady which is proper and then you practice okay don't worry about it let's go to the next question coming up on your screen this was NE 2016 velocity is given a and b are some constants what is the distance traveled between 1 second and 2 second here distance and displacement will be same okay so a + BT Square velocity is given displacement is asked displacement distance will be same because you are just going in a straight line you are not turning that's the reason why distance and displacement will be same and displacement we just saw is Delta X and Delta X if I want to know it from velocity 100% I have to integrate it from some limits T1 to T2 do I know velocity yes what is the velocity it is a t + BT squ okay but wait a minute do I know also the values of T1 and T2 yes I think it is given 1 second and 2 second so this is 1 this is 2 oh Whenever there is plus I can just separate them out whatever constants are there I can just bring them out of the symbol of integration so T into DT from 1 to 2 plus b is outside integral of t² DT again 1 to 2 again 1 to 2 that's all Now integrate T Now integrate T what will it become a is there as it is T's integration this is actually T to 1 so it will be T 2 by 2 limits are 1 to 2 plus b as it is T s's integration so T ra to 3 2 + 1 upon 2 + 1 limits are 1 to 2 this will become a into first put 2 then put 1 so 2 2 by 2 - 1 2 by 2 + B into first put 2 so 2 Cub by 3 then put 1 so 1 cub by 3 so this will become this will become observe 2 S 4 4 - 1 3 so 3 a by 2 plus 3 a by 2 + 2 cube is 8 8 - 1 7 so 7 B by 2 3 a by 2 7 B Sorry by 3 my bad 7 B by 3 that is there in option number B for biology option number two yes there you go P for basarat sir correct very good very good so these were some questions on derivatives and integration we have also seen those graphs position displacement velocity all those things so we'll just straight away go to some questions also which are asked in neat okay look at this displacement time graphs are given displacement time graphs are given for two moving particles at 30° and 45° with x-axis the ratio of their velocities the ratio of their velocities is the ratio of their velocities what do you do when graph is given what do you do when graph is given and you are asked to find velocity well velocity was DX by DT it is also nothing but tan Theta if you remember when it is a position versus time graph yes this is position this is time graph definitely the tan of theta will give you the answer so it's just basically you have to take tan 30 uh you have been asked the ratio of the velocities V1 by vs2 will be tan 30 by tan 45 because ratio is asked tan 30 is 1 byun3 tan 45 is 1 so answer will be 1 is to < tk3 1 is < tk3 is option C for Captain is option C for captain no it is not D I think you U Mook it for something else yep it is option number c okay uh if you have done it the reverse way you will get it as root3 by 1 okay great moving on to the next one coming up on your screen here it is aipmt 2008 question a particle shows the distance time graph as shown the maximum velocity of the particle is around which point the maximum velocity is around which point now remember whenever we say velocity it is DX by DT this is again X versus time graph correct so it is also tan of theta this Theta is the angle made by the tangent and the horizontal if you draw a tangent here it is like this if you draw a tangent here it is like this if you draw it here it is like this if you draw it here it is like this where is the angle maximum where is the angle maximum obviously I think the angle is maximum at C so Theta is maximum at C so velocity is also maximum at C point so answer will be B for biology B for baswaraj sir which is option number C or Point number c sorry point is C option is B point is C option is B is that right okay shall we go ahead to the next one coming up on your screen here it is velocity graph is given with time question is find the distance traveled think it's going in a straight line there is no turning or whatsoever so the distance will be the same as the displacement in this case so whenever we talk about displacement and velocity time graph is given velocity time graph is given recollect from velocity I want to find displacement or change in position or change in position you have to basically find the area under the velocity versus the time graph so how much is that area that's all you need to find so let's find it out it's not that difficult first look at this area it's a triangle so half into base into height which is 20 so it will be 10 this one is a rectangle height is 20 base is 1 so 1 into 20 which means uh 20 okay then there is a small triangle over here small triangle over here half into uh base is 1 height is 10 so this will be five this is a small rectangle here height is 10 base is 1 so 10 into 1 which is basically 10 this is also rectangle here 1 second height is 10 so 1 into 10 which is again 10 now just add these numbers you have 10 here then 5 here then 10 10 10 and 20 sorry 10 10 and 20 just check this out 10 10 20 yes perfect so what will this be my dear students 30 + 20 50 55 so 55 should be the answer is there 55 in the options yes it is 55 M perfect basarat are becoming very popular in today's session very good easy pey L szy just have to find the areas awesomeness awesomeness cool now let's go to the equations of motion and the freeall motion are you ready for the last two topics yes let's do this these are the two major topics which are generally asked more than derivatives most of the times these questions are asked and these are very simple straightforward things so equations of motion what do you mean by equations of motion or just in general they are also called as kinematic equations kinematic equations kinematic means this word means not rather you are interested in how things are happening how where when Etc you not interested in why they are happening Why did the the body move why did it stop you're not bothered you just okay is stopping I don't care where will it stop when will it stop when will it have this speed at what time will that have moved this much amount these are the things in question and these questions can be answered bya kinematic equations and these kinematic equations are very very important and they can be only applied in certain conditions just like imagine there is a car imagine there is a car it has some initial velocity it has some initial velocity I will call it U after some time maybe that car okay has some final velocity has some final velocity let's say we call it V maybe the car is accelerating maybe in this time the car has traveled some distance s this was at T is equal to0 this is at sometime t I can write four equations I can write four equations and these equations are only and only valid if acceleration is constant this is the most important thing only if acceleration is constant then and then only I can write four equations what are those four equations V is U + a final velocity is initial velocity plus acceleration into time second equation is displac is UT + half a s u is initial speed a is acceleration T is time V is final velocity s is u +/ a t sare third equation is v s - U sare is 2 s v s - U sare is 2 s and the last one is SN displacement in nth a second is U + a by2 2 N minus1 I'll explain this these three are straightforward we'll see direct examples but what is this displacement in the N second okay just imagine you are moving like this you are having some acceleration and they ask you displacement in nth second means when the time was n you go 1 second behind that means nus1 in that time whatever displacement you do in that previous second that is called as the displacement in the n second that is called as the displacement in the nth second let me give you an example if I say displacement in the fifth second means you are traveling at some point T was 5 go 1 second before that means T will be 4 so this is what I'm referring to this is what I'm referring to how much is this displacement in the fifth second similarly if I tell displacement in the uh 3.5 second 3.5 second sometime time will be 3.5 go 1 second before so time will be 2.5 so whatever amount you moved in that previous second is the displacement in the 3.5 second 3.5 second is that okay so these are the basic kinematic equations these these are the equations of motion or I would say the kinematic equations and they are only valid if a is a constant number see if a is not constant then I cannot use these These are only valid when a a a everywhere is constant if time is given most likely you'll be using these two equations if only displacement is mentioned or asked most likely you'll be using these equations if n second displacement is asked 100% you'll be using this equation so depending on the application what is given what is not given accordingly you will use different equations if final velocity is given initial velocity is given acceleration is given time is asked immediately you will go to First equation if initial velocity is given acceleration is given time is given displacement is asked immediately you will go to second equation if time is not mentioned initial and final speeds are mentioned acceleration is asked since time is not given final initial speeds are given acceleration is asked or displacement is asked you will use third equation so depending on what is given what is asked accordingly you will switch from one equation to other you cannot sit and by hard oh this happens then I'll use this no see from problem to problem that's all I would say see from problem to problem okay cool so there are sometimes these kind of questions where you know a car is moving and then suddenly it sees some obstacle and when how how far does it take to stop so you might have experienced this whenever you see an obstacle you always take some time to react you always take some time to react meaning suddenly somebody comes immediately you won't press the break there is some delay maybe 1 second delay half a second delay so even in that half a second delay what happens is the car keeps moving the car keeps moving after that you take some time to react your foot has to rise and then you have to press the brake or you have to take some time to react and then press the brakes after that when you press the brakes that's when your retardation will start that's when your retardation will start understand so always the total stopping distance is the reaction distance plus the breaking distance in the reaction distance in the reaction distance is understand your velocity is still going to be the same only your velocity velocity is still going to be the same it's only after this point does your velocity begin to reduce slowly till you stop till you stop here you basically decelerate here you basically decelerate till this point your velocity is the same after this your velocity begins to reduce that's what happens correct yes let's have a water break quickly great now if Reaction Time reaction distance is not given and don't bother then directly consider breaking distance you should understand pandu is driving the car if pandu drives the car he's very quick very smart his reaction time is fraction of a second immediately reacts tuck will put the brake and immediately the car will stop so in that case reaction distance will not be there he will not travel that extra mile or extra distance immediately he will break so some problems reaction time is not given which is okay don't worry about it let's solve some questions you'll get a hang of it look at this a car is going with some speed it can be stopped by some Force after 20 M if now the speed is 30 how uh much distance will it travel before it is stopped or it will be stopped by this force in how many meters that's the question let's visualize whenever kinematic questions come now you should always visualize draw the diagram you should always draw the diagram okay let's draw the diagram first case in initial velocity was 10 m/s there was some retardation acceleration was opposite so the velocity reduced reduced and it stopped finally became 0 m/s how much distance did it travel 20 m in the next scenario the velocity was little bit more 30 m/s obviously that person will travel little bit more distance till he stops force is the same so retardation will be the same but now the question is what is that displacement what is that displacement time is not mentioned speeds are there I feel we should use the third chematic equation V sare - u s is 2 s yes or no so let's use that let's use that v² - u² is = to 2 what is final speed he stopped so zero what is initial speed it is 10 what is acceleration well that is negative so or 2 into - A why is it negative because he's retarding he's breaking he's decelerating what is the displacement that is 20 do you understand why this negative is there because of breaking so this will become - 100 is equal to - 40 a - 48 okay I'll just keep it as it is I won't touch anything all right or I can just put 100 is equal to 408 I'll just keep it as it is I won't do much now let's do the same thing over here also here final speed is zero initial speed is 30 so v² - U ² is 2 into a into s s only I don't know so acceleration also is negative by the way because you're retarding so minus a into s so this will become -900 is equal to 2 a s with negative sign or 900 will be equal to 2 a s I don't know a but I want to find s let's divide both of them so 900 over here and 2 a into s over here and at the bottom I will have 100 over here and I will have 40 a over here do you see what and all is getting cancelled do you see a a got cancelled two got cancelled with 40 this became 20 this this this this got cancelled so what will my final answer b s will be 20 into 9 which is 180 M 180 M which is uh option D for am Delhi D for as Delhi very good Perfecto Perfecto got it how to solve this question this was application of third equation sign of acceleration was negative because it was retarding that was another thing always draw the scenario you will understand which equation to use that's why I said never buy by heart any problem draw see what is given see what is asked immediately it will click which equation has to be used another similar question two trains traveling on the same track in the opposite directions with the same speeds they begin to decelerate simultaneously when there are two kilm apart and they just have to stop so that they do not Collide question is what is their retardation going to be this is a standard common question guys let's see if you guys are able to figure this out start with the diagram without diagram do not proceed at all so there is one train here which is coming up with how much speed 40 m per second this is also coming over here with 40 m/s the total distance between them is 2 km this train also decelerates this train also decelerates this train will finally stop here this train will just avoid the collision by stopping here it will exactly be at the midpoint it will be exactly in the middle so 100% this much distance will be 1 km this much distance is also 1 km or 1,000 m one and the same thing 1 km or th000 M oh I think I know what to do now in 1 kilomet or 1,000 M the train has to stop this is initial speed final speed is zero distance is 1 kilm so the obvious choice of equation will be v² - U square is 2 what is the final speed when you stop zero what is the initial speed it is 40 what is the acceleration I don't know that's what I have to find out what is a displacement it is 1,000 okay but it is retarding so minus it's retarding so minus so 40 minus minus cancels 40 square is 1,600 so this will be 2,000 a 0 0 0 0 cancels so a will be 16 by 20 divided 4 so it will be 4X 5 which is8 m/s Square 8 is again am Delhi wow very nice8 is am Delhi again got it my dear Warriors Perfecto so these kind of questions are very very common my dear students based on kinematic equations let's solve some more questions I hope yes there are many question initial velocity of a particle is given it is 10 m/s and retardation is 2 distance moved by the particle in the fifth second is how much Fifth Fifth means n there is only one formula there is only one formula SN is U + ax 2 2 N -1 I gave you this formula right over here I told you right over here this is the formula U + a by2 2 nus1 so just U use that formula and you will get the answer what is the initial speed the initial velocity is 10 so U is 10 what is the acceleration 2 but it is retarding so minus 2 retardation is 2 so that means acceleration is -2 by 2 2 into what is n n is fth so it is 5 - 1 so this will be 10 minus uh 10 - 1 so this will become 1 meter so 1 m is a for a just a for as doesn't matter which as you go to no it is not B question is not displacement question is displacement in the fifth second fifth second so it is not B be careful some of you made a mistake some of you made a mistake they got excited they wrote B no it is not B it is option A your journey is for as now you went somewhere else okay let's go to the next question coming up on your screen here it is a particle goes in a straight line with constant acceleration velocity changes from this value to this value in this much meters find the time let's draw the scenario always it is very helpful its speed is 10 m per second and in a matter of 135 m the velocity becomes 20 m/ second acceleration not known time also not known question is find the time hm acceleration also not given time also not given can we solve this question maybe let's in fact find the acceleration using initial is known final is known displacement is known using this equation v² - U sare is 2 as s final speed 20 initi initial speed 10 acceleration I don't know displacement 135 this is 400 - 100 so might as well write it as 300 so 300 is equal to 2 into 135 that's 270 a 0 0 cancels so a will be 30 by 27 divide by 3 this will be 10 divide by 3 this will be 9 so 10 by9 m/s square is the acceleration that's not the question question is find a Time V is U + a I think that will work V is U + 80 this will work final velocity is 20 initial velocity is 10 acceleration is 10 by 9 and this is T 20 - 10 10 so 10 is 10 by 9 into T 10 10 cancels so time will be 9 seconds this time it is Captain this time it is Captain stus yes very good yes arat we had to use is U plus a isn't it amazing very good guys let's go to the next question let's go to the next question and that is on freeall motion this is the last part of the chapter where you apply kinematic equations in a specialized scenario where you throw an object either up or you drop an object from the b top to the bottom or you throw it up it goes up and comes down or you throw it down with some speed all these sorts of questions come in motion under freef fall which is actually Motion in one day think why because when an apple Falls it is traveling only in one dimension along a straight line when you throw a ball up it is going up and it is coming down it's also a motion along a straight line I'm not throwing it at an angle if I throw it at an angle it becomes projectile motion so it's motion under straight line only yes uh no you can do it in the rough space and you can do it on the question paper also but usually question paper it is not advised you are advised to do it in the rough space or the rough sheets they give you that rough space or the rough sheets okay so don't worry don't try to do it on the question paper you are not also supposed to do mental calculations because there are good chances that you might make many many mistakes okay now anything and everything which is left on the surface of the Earth anything and everything which is left on the surface of the Earth it will accelerate by meaning it will change its velocity that is called as acceleration due to the gravitational force acceleration due to gravitational force that is basically G and the value on an average is 9.8 m/s Square which you can approximately call it Pi Square you can also approximate it to be 10 m/s square Pi is 3.14 pi is 3.14 so Square it it will almost be 9.8 or close to 10 so these are the standard values which you are supposed to know and the best part about acceleration due to gravity is it is independent of the mass which is dropped it is independent of the mass which is dropped meaning meaning if a person drops a ball from here and elephant is there and this elephant decides I want to jump so this is that elephant this is that elephant it decides it wants to jump this ball will fall down and it will fall down with an acceleration G if it takes some time to fall down even that elephant will take the same time to fall and the acceleration due to gravity will still be G mass does not matter a cricket ball and an elephant both will fall at the same time every time please remember we always neglect the air resistance air resistance is always neglected which is a very good assumption air resistance is neglected there is no harm in doing that okay air resistance is neglected cool till this point it is clear all right great now since it is accelerating with 9.8 m/s square and I might be interested in with what speed is it falling how much time does it take when I'm interested in where how much when that means it is kinematics that means I can use kinematic equations also acceleration is constant which is an essential condition for applying kinematic equations so that's why you see in kinat or in just freefall motion you will see applications of kinematic equations equation one equation 2 equation 3 that's how you find height time speed whatever is needed in that particular question so there are some variations two standard variations which you should know one second let me just bring it over here the first variation which you should know is this one you are at some level you take a ball and you throw it up with some speed you throw it up with some speed what happens is the ball speed begins to reduce begins to reduce begins to reduce and finally it stops and then it again starts to come down along the same path with increase ining velocity and hits the ground or the same level with obviously the same speed whatever time it takes to go up and whatever time it takes to come down will be the same please remember that the time taken to go up will be the time taken to go down will be the time taken to go down also the velocity while going up the magnitude of it will be nothing but the velocity while coming down basically this happens this happens because the motion the motion is symmetric the motion is symmetric whatever is happening while going up will happen while coming down but in the opposite direction because acceleration due to gravity is the same acceleration due to gravity while going up or coming down is the same that's the reason for that that's the reason for that is that clear okay so for these kind of problems at maximum height at maximum height what will happen because velocity is reducing reducing becomes zero for a moment and again starts increasing so at maximum height the velocity will be zero and this will be your maximum height this will be your maximum height is that right everybody with me good now before writing the equations I often ask my students this question when I throw a ball up as it is going up and then finally when it is coming down what is the value of G is it positive or is it negative while going up is it positive or negative while coming down is it positive or negative you try to answer that in the chat box you try to answer that in the chat box what do you you think it is come on what is it is it positive or negative let me tell you the answer is depends what are you taking as positive direction if somebody decides this direction as the positive direction it doesn't matter whether the ball is going up or going down acceleration due to gravity acceleration due to gravity is always downwards always downwards so as per this sign convention because upwards is taken positive G will be negative G will be negative basically I will use I will use NE acceleration as minus G I use acceleration as minus G but if somebody decides no no no no I want to take the positive direction positive XA AIS positive y AIS downwards then for that person because G vector and this direction are the same acceleration will be plus G acceleration will be plus G so it all depends on which direction are you taking positive or negative what is that positive or the negative Direction you assume to be usually what happens is when the ball is going up you end up taking this direction as positive that's why you might have seen in school they say acceleration is negative when a ball is coming down usually we take downward direction as positive that's why you would have seen that's why you would have seen downward direction is taken as positive got it so it depends depends on what direction you have taken as positive or negative so let's solve this question to find the maximum height or the time of flight or whatever so let's say my aim is to find the maximum height to find the maximum height what do I do I will just consider the upward motion I'll just consider the upward motion my dear students I'll just consider the upward motion it started with u then the speed reduced and it basically stopped over here and the acceleration due to gravity was down and usually we take upward direction as positive direction so here is what we will do to find the height speed is given final speed is given cation is given time is not there so third kemetic equation so v² - U ² is = 2 a s final velocity zero initial velocity U acceleration is minus uh G because G is down assume direction is upwards into displacement is H so minus minus cancels so u² is 2 g h so H is u² by 2G this is a Formula which it is better that you remember it it's better that you remember it okay don't say that no sir I can derive it in the exam yeah you can but it's better you remember it you will save these steps save this time save this U energy that is how you find the height height is U ² by 2G next Formula that you might need is the total time of Journey you might need basically the total time of Journey that is also called as the time of flight time of flight now the total time of Journey is two times time taken to go up which is also two times the time taken to go down either you find the time taken to go up or you find the time taken to go down one and the same thing so again if you just consider the upward motion you throwing it with you let's take upward direction as positive we know acceleration due to gravity is down here you basically stop so using V is equal to U + a final velocity 0o initial velocity U acceleration minus G this is just the time taken to go up so therefore uh time taken to go up is U by G GT G comes down this is just time taken to go up so therefore the total time will be 2 times of that so 2 * of U by G this is another formula which you might need there's another formula which you might need and obviously this is the standard thing time taken to go up is twice the time taken to go up or down sorry total time is time two times time taken to go up or two times time taken to go down okay if just time taken to go up is asked it will be U by G time taken to go down is asked it will still be U by G total time is asked it will be 2 U by G clear let's go ahead let's go ahead okay one more type of variation which comes one more type of variation which comes is when you drop a ball from some height from some height and after that height it has some velocity it has some velocity and by the time it reaches here you dropped it at T is equal to0 it reached here at some time T question will be to find this time to find this velocity and obviously the acceleration due to gravity will be downwards the acceleration due to gravity will be downwards and usually in these kind of questions downwards direction is taken as positive because everything is happening down only usually so what will you write equation wise let's start so first thing is to find velocity is to find V what do we do I know initial speed I know the displacement I don't know the time I know the acceleration I want to find V okay I think I'll use v² - U ² is equal 2 a s final speed I want to know initial speed drop drop means I release just starts from rest so that's why zero so understand whenever that word drop is used it means it was at rest it released from rest that's what it means is equal to 2 into acceleration is down assume direction is also down so it is positive don't take it as negative displacement is H so therefore V will be root of 2 GH this is the formula V is root of 2 G is that clear if total distance is asked yes sha Prasad in the previous part then the answer will be 2 H because it will go up H come down H distance will be 2 H displacement will be zero displacement will be zero if total displacement is asked okay good then what about time to find time if you want to find time what do you do which equation will use I think second kemetic equation will be better S is UT + half a t² my displacement is H and it is down and downwards is also positive initial final displacement is down positive is also down so that's why plus h plus h initial speed zero no worries about the first term half into gravity is down positive is also down so plus G total time t Okay so H is GT s and that two can come up so basically t² is 2 H by G that means time is root of 2 H by G that is provided you dropped it provided you dropped it time is root of 2 H by G okay these are some formulas which you should should know this height formula you should know about what how the sign works you should know this concept that air resistance is neglected mass does not decide the gravity acceleration you should also know about uh height formula time of flight formula uh speed at the bottom and also the time taken to reach at the bottom under these conditions if you know this then you have a uh good knowledge about Free Fall motion and if the problem is not any of these then you have to come back to kinematic equations okay if it is not based on these conditions you have to come back to kinematic equations yes yes now there are some important points which you should know regarding this gravity always acts down irrespective of whether the particle is going up and down we just discussed this even when the particle is going up gravity is down even when the particle is coming down gravity is down so gravity is always down magnitude we have spoken about 9.8 10 can be taken approximately at the top Point velocity becomes zero upward and downward motion time taken to go up and down is symmetric we have seen that you can choose upward and downward Direction positively according the sign of G will change we have seen this also we also seen choose positive direction in the direction of the motion preferably but there is no hard and fast Ru usually wherever the ball is going usually that direction we take it as positive now sometimes you will see in neat they have asked these questions many times actually Galileo's law of odd numbers which says that the distance covered by a falling object in successive time intervals is linearly proportional to odd numbers what does this mean it means if you drop a ball you let say wait for some T seconds this is t equal to 0 this is T is equal to 0 this is T is equal to t you have traveled example X you wait for some more time and exactly the same time that means now the time is 2T you would have traveled 3x you travel for m t seconds so the total time will be 3T here this will be 5x next will be 7x next will be 9x in equal intervals you travel distances in the odd numbers ratio you travel distances in the odd numbers ratio this is what Galileo is laws this is what Galileo's law is exactly this can be also used for even horizontal motion you start from rest you start from rest if you travel X or accelerating like this then after sometime you will travel 3x after some time you will travel 5x after some more time you will travel 7x and so on and so forth so displacement in the first second is to displacement in the second second to displacement in the third second second and so on and so forth will be always 1 is 3 is 5 is 7 that's how it goes OD numbers ratio this is gulio law it is very very helpful for solving many many questions directly I will show you I will show you look at this uh where is it I think I put that question somewhere yeah I'll come to this question and then we'll go go back to that one a particle is starting from rest uh starts with rest okay and moving constant acceleration X is in first 2 seconds Y is in next 2 seconds then how is y related to X in the first 2 seconds it is going X so in the next 2 seconds how much will it go 3x so obviously this 3x will be y obviously this 3x will be why because if you wait for more 2 seconds then it will go 5x distance it's Galileo's law so hence the answer will be Y is equal to 3x hence the answer will be option C Captain stus Y is equal to 3x got it in fact this question was also repeated here in need 2022 ratio of the distan is traveled by a Free Falling body in 1 second third fourth is Galileo's law 1357 that's all directly C for Captain sh directly so you can see so many questions directly can be solved from your Galileo's law of odd numbers only valid for only valid for constant acceleration and equal intervals of time equal time interval should be there otherwise it won't work 2 to 2 seconds 3 3 3 seconds 1 1 1 second like that then this question was asked in NE 23 let's see if you guys are able to solve this particular question nice question a bridge is built a student throws a ball up with some speed ball strikes the water second water after 4 seconds the height of the bridge about the water surfac is let's visualize this what is happening so this student is standing on a tall bridge and there is water over here in fact this height only is not known to me and what he does is he throws a ball up with how much speed he throws a ball up with how much speed 4 m m/ second okay 4 m/s so it will go up for some time and then it will fall down over here and it falls down over here at T is equal to how much seconds 4 seconds question is find the height well in this problem I know acceleration due to gravity is down it's up to me whether I want to take upwards as positive or downwards as positive I feel since it is eventually going down let's take downwards only as positive let's take downwards only as positive always assume positive and negative or else you can make a mistake in the science which equation I might need displacement is asked time is given so only one equation second equation that is s is UT +/ a squ so I think we should go to S isal UT + half a t² from here to here that's the displacement don't take this distance no displacement from here to here initial to final what is the displacement it's h what is the initial speed it's four but it is opposite to the positive direction so it will be Min -4 did you understand why minus 4 this four is opposite to the assumed Direction that's all what is the time 4 plus half acceleration due to gravity is down in the assumed Direction so it is + 10 and time is again 4 so this will become -6 + 5 into to 16 so this will become 16 5 80 so this will right - 16 + 80 so this will become 64 M so height will become 64 M which is option D perfect that is the answer this was asked in need 23 just last year crazy right understood how to solve these questions Perfecto shall we go ahead shall we go ahead okay next question coming up on your screen we Sol these two already this is ncrt exercise question a ball is thrown up okay from the top of a multistory building the height of the point from where the ball is thrown is 25 m above the ground how high will the ball rise how long before it hits the ground okay let's draw the diagram first it's very similar ncrt question again this is the ground surface the ball is thrown like this with what speed 20 m/s 20 m/s and this height is 25 M from here to here that is what is given obviously acceleration due to gravity will always be down you can take downward direction also as positive just for your sake okay it goes and it's over here after some T seconds question first one is how high will the ball rise how high will the ball rise this part this part how high will the ball rise you can solve it like your normal standard question uh like this one over here where did it go like this one it's starting at a point it's going up and coming down so how high will it go using this formula u s by 2G can I just use that formula u s by 2G yes or no my dear Warriors so let's just use that so H will be directly u s by 2G so U is 20 G is 10 so 400 by 20 which is again 20 M so height is 20 M that's the first answer of this particular problem okay very good what next what next my dear Warriors think about it what next what will you do how long will it be before the ball hits the ground how long will it be before the ball hits the ground so for this part for this part which equation you will need which equation will you need think about it time is asked displacement is known most likely most likely it is better to use the second equation which is s is UT + half a t² from here to here I'm going down initial final straight line joining initial and final point is displacement and downwards is positive so it is + 25 initial speed is 20 but up downwards is positive so - 20 into t + half acceleration is down in the positive direction so 10 time I don't know okay so this will become 25 is = - 20t + 5 t² 5 5 5 I cancel so 5 will be equal to - 4 t + t² it's a quadratic equation so t² - 4 T bring that 5 over here - 5 is 0 so therefore t - 5 into t + 1 I just factorized it- 5 + 1 - 5 into - + 1 is - 5 - 5 + 1 is - 4 is equal to 0 so therefore T will be five uh or it will be minus1 but we all know time has to be positive time can't be negative so this is ignored so the time is 5 seconds so the time so the time will be basically 5 Seconds that's the answer let's check it out yes 20 M and 5 Seconds 20 m and 5 Seconds got it everybody with me I know your test is going to start let's do the last question now let's do the last question now coming up on your screen after this you can start attempting your test your Victory mock test the link is there in the description box below okay let's do this a stone is thrown vertically down uh with a velocity of this much from a top of a building reaches the ground with this speed what is the height of the building need 2022 question it is thrown down with a speed of 40 and uh height is not go given so height I'll just assume it as H but after coming down the velocity is how much velocity is how much uh 60 so this is 60 m/ second and acceleration due to gravity obviously is down let's also take downwards only as positive because everything is happening down only why do you want to create unnecessary trouble time is not given velocities are there displacement is there acceleration is there the only equation is third equation which is v² - u s is 2 as s final speed 60 initial speed 40 acceleration G down so positive displacement H this is 360 0 - 160 0 is equal to 20 H 36 0 - 160 0 that is nothing but uh how much that is 2,000 is equal to 20 H 0 0 cancels and this 2 two also cancels so this will be 100 m just check this out 100 m yes perfect that is the answer 100 m correcto very good D for am Deli perfect perfect my dear students now I have also kept the points to point over here from ncrt like we say the session is from ncrt and neat always will refer to neat people will always refer to ncrt they will make the questions also from ncrt many intext and exercise questions back exercise examplar questions will just be directly asked many times by changing some small values here and there sometimes they just pick the lines from summary or points to P or the main points directly from definition or even the problems are directly picked many times by changing small values so that's why it's very important you uh for sure you go through the points to point out or any details which are there in ncrt okay so these are pretty much straightforward I have done almost all these things like say for example let's go through it very quickly origin and the positive direction are a matter of choice yes we have done this point how you choose the origin where you want the origin to be which is positive which is negative it's up to me that is what it is about and you can choose your own sign convention accordingly the answers will come out perfect then the next point is all about particle is speeding up acceleration is in the direction of velocity if its speed is decreasing acceleration is opposite to that this makes sense if acceleration and velocity are in the same direction versus velocity is here and acceleration is opposite to that here when they are in the same direction then the speed is increasing whereas when they are in the opposite direction then the speed is decreasing makes sense like when you throw a ball up acceleration is down velocity is up speed is decreasing when it is coming down speed and velocity sorry velocity and acceleration same direction so speed will increase so that is what the second point is all about that is what the second point is all about the sign of acceleration does not tell whether it is speeding up or speeding down whether the speed is increasing or decreasing this is very important the sign of acceleration does not tell anything because it depends on the choice like sometime back I told you whether G is positive or negative many people said sir it is positive while going up or coming down negative while going up no it depends I can choose G to be positive or negative it's up to me how I took positive direction depends on me so my choice will decide the sign of G so how can you say the particle is accelerating or decelerating getting my point so while going up it is reducing the speed but is the value of G negative or positive depends how I take directions so acceleration sign does not decide whether it is increasing the speed or decreasing the speed that is what this point say and this is what they have explained this is what they have explained okay in big text okay if a particle is falling under Gravity the acceleration though negative results in increase in the speed makes sense even if when the particle is coming down if you take upwards as positive gravity will be negative but in spite of that the speed is increasing so how is the speed increasing when G is negative so that's what it says it don't go by the sign of acceleration see whether acceleration and velocity are in the same direction or in the opposite direction same direction speed increases opposite direction speed decreases okay zero velocity at any instant does not mean zero acceleration makes sense zero velocity does not mean zero acceleration just like at the topmost point is the velocity zero yes is the acceleration zero no it is still acceler ating only for that moment it stopped next moment it is moving it is in fact increasing the speed so acceleration has not gone it is still there it's just that it has changed the direction at that point so that is the fourth pointer in kinematic equations the various quantities are algebraic they may be positive or negative they are applicable in all situations with constant acceleration very important the kinematic equations are only applicable for constant acceleration and they are algebraic meaning they can be positive or negative you have to choose proper sign convention you have to choose proper sign convention that's what it means right we have done that instantaneous velocity accelerations are exact and are always correct when while the kinematic equations are true only for the motion in which the magnitude and direction of acceleration are constant during the course of motion the definition of the velocity and the acceleration okay so don't worry about this uh we have not gone through these equations as such I mean I have given you much simpler equations they have tried to confuse you uh with those equations in equation 2.1 and 2.3 the point is that uh you know when you write when you write uh acceleration is you know final velocity minus initial velocity by time this is valid this is valid only when this acceleration is constant only when this acceleration is constant else how can you say this final velocity minus initial velocity by time because every instant acceleration might change so this is only valid they are only true for the motion in which the magnitude and the direction of the acceleration are constant only when the acceleration is constant then you can use this if it is not then it will keep on varying because you know it it will just give you average value then it will not be instantaneous value it is kind of obvious correct very good so these are the pointers which were there please join the telegram group there are quizzes test links everything which are shared and PDFs everything will be available only on the telegram Channel and if you watch the lecture till the end I hope you will put up chapter to complet it okay so the next chapter that I'll be doing is um waves chapter okay but yeah if you're watching it recorded you can watch it in any manner or any order that you want many students were asking sir please do uh oscillations and then waves and all of that because I think it is coming up in your uh pre-board or whatever in your final exams of 11th and all those things so let's do that yes in the days to come oscillations and then waves okay and we'll slowly complete as many chapters as possible okay so see you in the comments down there thank you for liking if you're not yet liked please do that right now that's your Guru D yep do that thank you thank you so much for liking and yes subscribe to the channel as well thank you so much all the best for your test test link is there below it's a free of cost test Victory test only available for today after this the entry is closed and you will see the price goes up to 1,000 rupees thank you very much bye-bye as Vista sir signing off bye-bye