[Music] hey all welcome to homeschool hope everybody are doing good and i am back with class 11 physics series and i am with the most requested chapter of class 11 that is motion in straight line so today we will discuss few aspects of motion in straight line see this is the most important chapter of class 11. you should definitely concentrate for board point of view as well as for competitive point of view okay so uh let me give a complete concept clarity on all major concepts of motion in straight line so we all know the meaning of the word motion right so what do you mean by motion here motion is a moment right it is a change in position with time is called motion see i am standing here and i move see my position is changed i was there now i am here and this change in position took place with respect to time yes i know so i was here i moved here in some fraction of time so this moment of an object with respect to time is called motion okay so what is motion here change in position of an object with the time is called motion right fine and this chapter is all about rectilinear motion okay so what do you mean by the word rectilinear motion rectilinear motion in the sense motion in straight line motion in straight line or we can also say motion in one dimension okay so such a motion is called rectangle motion say i am here and i move only in one dimension right so motion in straight line this is an object if this is moving like this or if this is moving like this or if this is moving like this say how is this object moving it is moving in a straight line so motion in straight line or motion in only one dimension is also called with the name rectilinear motion okay so this is the physics term rectilinear motion fine so we got to know what is this motion right say here this chapter is all about various terms that describes motion okay say motion can be described motion can be explained with the help of lots of terms like distance displacement okay displacement distance the difference is very important and i will give that a difference today in this class and then it can be described with the help of a factor called speed and there is another factor called velocity and there is one more important factor acceleration okay so mainly motion in a straight line or motion in any direction for that matter can be described with the help of these terms so the entire chapter is about understanding these terms okay and calculations involving these terms right so hope you got cleared with the concept what we are actually studying in a chapter fine in today's video i am giving an entire uh explanation or description about the distance displacement then we have something called speed average speed then we will go for average velocity and new miracles related to these concepts okay so this is all about today's class so you guys now understand the concept very clearly that there is lots of difference between distance and displacement okay say for example you have a ball here right and a ball from here it is moving here right so this is the initial position of a ball usually uh you know what position is denoted with the letter x here okay so whenever i write x it means that position right okay so this is initial position of a ball say let me write it as x i and this is final position of a ball let me consider as xf okay and how can a ball come from this initial position to final position it may take various routes it may take various paths isn't it say from here the ball may take this path and can come here or the ball may take this path and can come to this position right and there are several ways or several paths that a ball can take to come from initial position to final position right and and this is what this path length which we call it as distance okay say what is this this is path length length of a path path length okay what do you mean by this length of a path is called path length which is nothing but we can call it as distance okay so this is the path length or distance one and this is the other path length and uh you know this is also a distance two okay so this is first path and this is the second path and this match is the length of the first path so that length of a path which we call it as distance okay so this is one distance this is another distance right and now what is displacement displacement is this distance okay displacement is what change in position is called displacement okay so how do you mention change in position change in position how do you represent that means change change anything uh you know mathematically or in physics and chemistry we represent with this delta delta means what change change in what change in position that is delta x which is equal to final minus initial right so final position final position minus initial position okay so this is how we normally calculate displacement and this change in position which we will call it as displacement this is what we mean by displacement okay so hope you are clear with the difference between distance and displacement distance is what path by an object that it has traveled okay so it is that path length which we will call it as distance whereas whereas this one this one okay change in position initially ball was here and finally ball is here and this distance okay this change in position is what we mean by displacement okay so in the name itself we have place place place means what your place has changed okay say initially it was here finally it is there place is changed so that distance that change in position we will call it as displacement okay fine and let us understand this with one more example suppose you have a ball okay all uh there's a person who is moving eight meters this way okay and again this person is moving two meters this way right and finally the person arrived here person initially moved eight meters in a forward direction again from there he moved two meters in a straight line okay and this is initial position of a person and this is final position of a person can you tell me how much is the distance how much is the distance he has traveled initially person was here he moved eight meters and then from there he moved again two meters in a uh straight line okay so the total distance i can say here total distance is equal to eight meters plus 2 meters that is equal to 10 meters so the distance is a path length okay in which a person has moved from this point to this point so total distance he moved was you know 10 meters but what about the displacement in this case person was here and final position of a person is this right so displacement how do you calculate displacement displacement right which we can call it as delta x is equal to final position of a person x f minus x i right the person is standing after 10 meters right so 10 meters minus initially it was a 0 meter so 0 meter so here also 10 minus 0 10 meters so displacement is also 10 meters distance is also 10 meters so in this case distance was equal to the displacement does every time our distance is equal to displacement no okay you observe this example observe carefully see you you you have a car you have a car right and it is moving two meters this way and from here the car is moving uh four meters this way and it took a u-turn and it has come back you know two meters backward right to meet us backward say in this case can you calculate how much is the distance and displacement right you observe the question here this is question two or example two car moved two meters this way again from here four meters forward and later it took a u-turn and it is moving backwards that is two meter back so how much is the distance here the distance the total path two meters plus four meters plus two meters okay i'm worried about the total path okay i'm not worried about the direction of whatever it is right so just the total path the total distance the car traveled all together is two plus four plus two that is eight meters so this is your distance but what about displacement what about displacement right observe carefully two meters plus four meters yes so this much okay minus the car is moving backwards right so minus 2 meters minus 2 meters so how much is your displacement 6 meters minus 2 meters that is equal to 4 meters you see the displacement is 4 meters and distance is 8 meters so every time displacement is not equal to the distance actually the distance is always equal to or greater than displacement okay so this point is very very important take it as a note guys distance your distance is always either equal to or greater than displacement greater than displacement so this is really very very important and one more point i would like to mention here distance is scalar distance is scalar quantity okay whereas displacement is vector quantity displacement is vector quantity okay so what do you mean by scalar quantity a quantity which has only magnitude we don't bother about direction here okay see distance distance you see we only consider the magnitude i mean the total path that a car has covered right so that is the amount magnitude means what amount or the total path that a car is covering we don't worry about the direction right so distance is a scalar quantity whereas displacement you know when you come to displacement direction also matters a lot any see the car was here it came here again it took u-turn and now the position of a car is this so this much is your displacement right hope you're getting my point what is the displacement displacement is final position minus initial position right initially the car was here but finally after it took u-turn and came here and this is where the position of a car so definitely you will not have a displacement two plus four plus two right so you will have a displacement 2 meter plus 4 meter minus this much this much you should take it off right so that is how we will calculate displacement okay so direction is also very important we consider direction for the displacement so the quantity which has both magnitude and direction is called vector quantity so this is the most important basic idea one must have distance is always a scalar quantity whereas displacement is a vector quantity okay and you know what displacement when you calculate you can either get a positive value or negative value so here every case displacement i had value in positive sign right but you will also have displacement in a negative sign okay so this sign actually tells you about the direction okay this sign actually tells you about the direction just try to understand this example that i'm showing on a board you see guys i have a x-axis where this is a 0 this is a point of reference see always any object when it is moving it should start from a particular point right so that point we will call it as reference point of reference okay fine and you know what okay so this is a one meter two meter three meter four meter and so on fine and you know i am actually here okay so i am here and i moved backwards okay and i moved i moved and i came here i came here so this is my final position okay and this is my initial position and can you calculate how much is the displacement here you see the displacement i'm calculating displacement so how do you calculate displacement uh x final minus x initial okay final position minus initial position which is my final position it's here that is 0.5 meters okay so my final position is 0.5 meters minus initial position is around 2.5 meters isn't it i i am exactly in between 2 and 3 right so 2.5 so what is the value i got i got around minus 2.0 meters you see the displacement the displacement is equal to minus 2.0 so displacement can also be a negative value okay so this negative actually tells you that the direction in which you are moving okay so this sign will give you an idea about in which direction you are actually moving so displacement is a vector quantity you need to consider the direction also but in this chapter we don't discuss too much about direction okay so we don't need to worry about this side okay so we only consider the magnitude of displacement okay so here the magnitude of displacement the mode of displacement mode means what it can be a negative or positive just the number is important for us right so magnitude of displacement is equal to 2.0 meters we say okay so just to make you understand that we will get a negative value for displacement uh i gave you this example say this negative or positive sign will actually give you an idea about in which direction the object is moving okay but as far as this chapter concerned uh we can neglect this signs and we only consider the magnitude of displacement okay just the number the digit we consider here right so this is all about the displacement and distance so this differentiation is very very important to understand guys and now i will go for speed and velocity speed and velocity okay actually we discuss average speed and average velocity i'll tell you what is the difference between average speed and the speed okay just a normal speed or uniform speed okay so usually speed is nothing but distance distance by time okay velocity is nothing but displacement by time displacement divided by time you can observe the difference between speed and velocity both are not same okay so speed can be calculated by this formula it is distance you know the distance is path length it's a scalar quantity right so distance by time is your speed and displacement displacement is a vector quantity right so displacement by time is our velocity okay and usually when an object is moving in a straight line uh in a same direction with constant speed okay if it is moving in a straight line with constant speed right without changing any variation in a speed if it is moving in a straight line in a same direction such velocity we will call it as you know uniform velocity uniform velocity okay so if the speed is uniform constant okay say for example a car is moving a car is moving in a straight road with the same speed then such a speed we will call it as uniform speed or or if you want to talk about velocity you will call it as uniform velocity but practically speaking uh you know what we don't observe uniform velocity see when a car is moving on a certain road you know we we increase the speed to some extent and then again we decrease the speed right so if a car is moving on a road right initially if if there is no disturbance on a road it moves faster right and again if there is a disturbance on a road you know it becomes little slow right so you know what uniform speed or uniform velocity is practically not possible right so you have ups and downs in the speed or velocity so we will talk about average velocity and average speed so what is important for us is average velocity average speed and average velocity okay so these are important factors for us average velocity is represented something like this v bar okay so average speed uh just you know speed doesn't have any symbol guys so if you want you can just consider this for average speed okay so what is the formula for average speed average speed is nothing but total distance by total time okay whereas average velocity is nothing but total displacement very very important total displacement by total time okay fine so we don't consider uniform speed and uniform velocity we always consider average speed and average velocity and we have calculations relating to average speed and average velocity right so what is average speed it is total distance by total time average velocity is total displacement by total time okay and definitely uh since total distance distance is a scalar so average speed is a scalar quantity so this is also very very important average speed is always scalar and average velocity is always a vector quantity okay so this is all about the concept of average speed and average velocity so now we will learn few examples how we can calculate this average speed and average velocity see the first example guys here there is an object which is moving with 4 meters per second this is the speed okay initially the object is moving with 4 meter per second speed for two seconds and it has come here okay and after two seconds the object speed is three meter per second and it went to the final position okay in five seconds okay so hope you can understand the question here see this is the speed of this object okay it has moved here with this speed in this much time and again from here the speed is changed here the speed is not 4 meter per second the speed is 3 meter per second and it is moved to the final position in 5 second okay so here you have to calculate what you have to calculate calculate average speed and average velocity both you need to calculate okay so what is the formula for average speed first we will try to calculate average speed so average speed is equal to total total distance divided by total time isn't it okay so total time is here two seconds plus five seconds right so total time is how much two plus five that is seven and what about the total distance what about the total distance calculate the distance here so what is the distance here we all know speed is equal to distance by time isn't it so speed into time will give you distance right so speed into time speed is four time is two so four into two photos are eight so eight meters is the distance this distance is eight meters and what about this distance three into five three fives are 15 so 15 meters is this distance so what is this distance it is eight meters what is this distance it is 15 meters so total distance is how much 8 meters plus 15 meters right so 8 plus 15 how much do you get 23 by 7 okay meter per second so this much is your average speed this much is your average speed okay so hope you understood how to calculate average speed here similarly if i asked you to calculate average velocity average velocity symbol is v bar so what is the formula for average velocity displacement displacement total total displacement divided by total time okay so this is your average velocity formula so total displacement is how much object was here finally it is here so total uh distance is equal to total displacement here okay so object is here now it is here so displacement is how much 8 meters plus 15 meters only so 23 meters divided by total time is how much 2 seconds plus 5 seconds that is 7 seconds so here average velocity and average speed is same isn't it i told you speed can be similar to displacement okay so average speed and average velocity is same okay but now you observe this example okay so here also you have to calculate average average speed average speed and average velocity average velocity both you need to calculate observe the question here initially the car is here and it is moving with the speed 10 meter per second for about four seconds okay with this speed car is moving from here to here in this time and again from here the speed has changed six meter per second it is moving here for about three seconds and again you know it's moving backward direction its direction is changed okay say uh with two meter per second speed it is moving in this direction right uh for about three seconds so you have to calculate uh you know average speed so what is the formula for average speed we know it is total distance divided by total time isn't it so how much is the total distance so distance we know distance is equal to speed into time okay so how much is this distance uh speed is 10 time is 4 so 10 force are 40 so 40 meters is this distance okay and then how much is this distance this distance is uh 6 into 3 that is 18 meters 18 meters is this distance and how much is this distance total distance you have to do right 2 into 3 two threes are six meters right so now we have calculated distance actually okay so how did we calculate distance the speed into time that is the distance okay fine so total distance is how much 40 meters right 40 meters plus 18 meters plus 6 meters okay divided by total time time four seconds plus three seconds plus three seconds right so this is how you will calculate so you will get around 64 by 10 that's around 6.4 meter per second okay so this is your average speed and coming to average velocity carefully you try to observe this diagram average velocity see what is this distance 40 meters what is this distance distance or displacement here distance is equal to displacement so instead of distance i can call it as displacement so this displacement is 40 meters this displacement is 18 meters whereas this displacement this displacement is 6 meters right so what is our average velocity it is total displacement divided by total time isn't it so how much is the total displacement i can do 40 meters plus 18 meters 40 plus 18 i can do but minus you see here the car is moving again backwards right say uh your final position of a car is some somewhere here so definitely you have to do 40 plus 18 you would have done minus 6 meters you must do minus 6 meters divided by total time is same right that is 4 seconds plus 3 seconds plus 3 seconds okay so how much is your answer you will get 52 by 10 that's around 5.2 meter per second so this is your average velocity you observe the values of average speed and average velocity here average speed value is greater than average velocity that means every time average speed is not similar to the average velocity okay speed is actually slightly it can be slightly greater than velocity so this point is really very important average average speed is always it can either equal to or it can be greater than average velocity velocity okay so this point is very very important so every time it need not be similar with average speed okay so average velocity can slightly be lesser than average speed right see this is first example where you can observe average speed is equal to the average velocity but here your average speed is not equal to the average velocity average speed was slightly higher average velocity is lesser right okay and now coming to another example observe this example so quite an important example here also same thing you have to calculate average speed as well as average velocity okay so first let me calculate average speed so average speed is total distance divided by total time so first you calculate the distance see this is object with 4 meter per second with this particular speed it is moving in this way for about 2 seconds again from here with certain speed it is moving like this for about 3 seconds so what is the distance here distance can also be calculated you you see here distance is always speed into time right so four into two so photos are eight meters is the distance and here what is the distance this much what is the distance 2 into 3 that is 6 meters is the distance so average speed total distance is how much 8 meters plus 6 meters divided by total time is how much two seconds plus three seconds right so this is how you will calculate average speed average speed calculation is much easier but what about average velocity okay calculation of average velocity you have to concentrate here this is the initial position of object and this is the final position of object and this much is your displacement isn't it this match this much is your displacement so this displacement so average velocity how do you calculate v bar is equal to total displacement total displacement divided by time right okay so time we know time is what two seconds plus three seconds that is five seconds is your time but what about the displacement displacement is this length this this this much length is what your displacement so how do you calculate displacement you see here it's it's making an angle 90 degree right so it has become right-handed uh triangle now so you can apply pythagoras theorem right so let me call this as yes displacement as yes so first i need to find out this yes so s square is equal to what what is this displacement what is this displacement eight meters so eight square uh plus six square right so what do i get s square is equal to uh i would get around 100 right so s is equal to square root of 100 so our s is equal to 10 meters so your displacement is 10 meters here okay so first we have calculated the displacement it has become a right angle triangle now so using pythagoras theorem we calculated the value of yes okay so yes is 10 meters now substitute here 10 meters divided by time 2 plus 3 that is 5 meters right so your average velocity is how much it is two meter per second two meter per seconds right so this is how you have to calculate if an object is moving in this particular way okay fine so anyway this particular concept we will use it uh much later and now we will see few numericals that have been asked in the previous board papers or in competitive examinations answer the first question guys actually from this question we are deriving one formula uh that formula can act as a shortcut to apply for many other questions so let us try to get that particular formula a person travels half the distance at speed v1 and rest half the distance with the speed v2 find average speed so always when the problem is given try to draw the diagram so that you get more clarity about the question okay so drawing a diagram is the most important ones you can understand the diagram half the problem is over remaining half is just apply the concept or select a suitable formula substitute calculate and give the answer so drawing a diagram is very very important here so a person so what is he doing he's traveling half the distance half the distance with how much speed with the speed v1 okay so this person is half the way he has not completed his travel he is half the way and this half the way he has come with this particular speed that is v1 and again from here he completed his journey he reached his final point with a speed v2 you see the speed is not same with some speed person traveled to half distance again he changed his speed right and remaining half the distance he has covered with the speed v2 so what is the total distance guys the total distance is d here total distance is d and what is this much distance half the distance means what d by 2 and what is this distance it is also d by 2 okay so distance from here to here is d by 2 distance from half the way to final point is d by d so what did they ask you to calculate they asked you to calculate average speed isn't it so just stick on to the formula here what is our average speed it is total distance total distance divided by total time total time okay so total distance we know it is d by 2 plus d by 2 isn't it d by 2 plus d by 2 okay fine and divided by total time so what is the time here so we all know speed is equal to distance by time isn't it so time is equal to distance divided by speed right let me call the time required for a person to come from this point to this point is t1 time required for a person to come from this point to this point is t2 so what is t1 guys t1 is nothing but distance by speed what is this distance d by 2 divided by v1 right and what is t2 d by 2 divided by v2 so time is what t1 plus t2 right so what is t1 and t2 substitute d by 2 plus d by 2 divided by t1 is how much uh it is d by 2 v1 plus d by 2 v2 so if you simplify this we will get 2 v1 v2 divided by v1 plus v2 so our average speed our average speed is equal to this is what we will get 2 v1 into v2 divided by v1 plus v2 so you just have to simplify this okay so when you simplify this is the final uh formula or you know the final quantity you will get actually this is important to remember if you can remember this you know uh similar problems can be solved very easily within a fraction of few seconds okay i will show you with one example where we can apply this formula so remember say whenever they mention something like this in a question see a person or object travels half the distance with some speed and remaining half the distance with another speed say if this concept comes into a question then you can always apply this formula say one example where we can apply this formula is this you can observe this question a car covers first half of the distance see there is a car and this car is covering first half of a distance with what speed with 40 kilometer per hour okay and remaining half the distance is covered with the speed 60 kilometers per hour see half the distance is covered with one speed and remaining half the distance is covered by another speed speed is not same here and you have to calculate average speed so average speed in the sense please don't take the average of these values don't ever do 40 plus 60 divided by 2 you will get 50 so 50 will be there as one of the option where that is the wrong option okay so average speed always you have to apply a formula right okay say how do you calculate average speed is equal to average speed is equal to total distance total distance by total time right okay and now you see here how much is the total decency say this distance let it be x and this distance let it be x okay so how much is the total distance x plus x x plus x so you will get 2x so 2x your is your total distance and coming to the time total time is what let the time taken for a car to move from here to here with this speed let it be t1 and here let the time be t2 okay and what is time here time we know it is distance by speed distance by speed so what is the distance x x divided by speed is how much 40 so what is t2 here distance by speed so distance is x divided by speed is 60 so x by 60 so substitute total time is how much t1 plus t2 know so what is steven t1 is x by 40 and p2 is your x by 16 okay so when you do this you can get your answer but instead of doing all such okay you can simply apply this formula see i'm showing this problem in two methods one is a direct method normal method okay by applying a logic or concept the other method is just this formula okay see they mentioned half the distance with one speed remaining half the distance with another speed then what is the quick formula that you can use 2 into v1 into v2 divided by v1 plus v2 right so what is v1 you take one speed as v1 and this as v2 right so what is v1 40 into 60 divided by v1 plus v2 v1 40 plus 60 okay so just when you do this you will get around 40 kilometers per hour as answered even when you substitute this you will get 40 kill 48 kilometers per hour as your answer okay so this is one method and this is another method say here just you have used the formula so if you can remember this formula it can help you to solve the questions in an easiest way or in case if you are bad at remembering formulas you can just apply the concept or logic and you solve it okay so in two methods i have solved this problem so answer is 48 kilometers per hour right and now we will go for two more questions coming to question number three which is one of the question from previous neet papers a car moves a distance of 200 meters okay so a car right and it from one place to it has come to another place and the distance total distance covered by this car is you know 200 meters right it has covered 200 meters it covers the first half of the distance with the speed 40 kilometer per hour and the second half of the distance with the speed v kilometer per hour that v value we have to find out guys we need to find out that v value here fine and then the average speed they have given average speed they have given that is how much 48 kilometer per hour okay so how do you do this first half of a distance with this speed second half of a distance we don't know that's what we need to find but average speed they have given can we use shortcut formula here say we have a formula average speed is equal to v1 v2 to v1 v2 by v1 plus v2 right say i will use this shortcut formula and i will finish off the question okay but i can show you the elaborate method also just understand the logic here fine so what is our average speed formula average speed okay let me show it here it's a elaborate method i'm showing you average speed is equal to total distance total distance divided by total time total time so total distance is how much total distance they have given 200 meters but you see the units of speed guys they have given it in kilometer per hour right so this meters convert it into kilometers right so i can take it as 0.2 kilometers right say 200 meters in the sense 0.2 kilometers divided by total time we don't know total time let the time of let the time for a car to move from this point to this point to be t1 and from this point to this point the time taken by a car is t2 so what is t1 so we know time is equal to what distance by speed right so distance is how much distance will be 0.1 kilometer half make it half point one kilometer and make it half point one kilometer right so time is 0.1 kilometer divided by 40 and t2 is 0.1 kilometer divided by v so what you will substitute time is t1 plus t2 right so what is steven 0.1 kilometer divided by 40 what is t2 0.1 kilometer divided by b right so average speed value they have given it is 48 so 48 is equal to 0.2 kilometers divided by 0.1 by 40.1 by v okay so just if you can solve it you will get the value of v okay so this is a normal method that you can go for based on the concept based on applying concept or logic okay but you see if i apply a shortcut formula just simple average speed is 48 right 2 into consider this as this speed as v1 this speed v2 we don't know v2 we have to calculate okay so 2 into how much 40 into v2 we don't know right so divided by v1 v1 is 40 plus v2 okay say by this shortcut formula also you can calculate this is much easier in calculation compared to this right so you guys you can calculate the answer and post to the answer in the comments okay so let me check who will post the answer first that's all about you know uh distance displacement average speed and average velocity the most important concept of this chapter and in my next class i will come up with the next concept that is acceleration and equations of acceleration thank you so much do subscribe our channel to learn the concepts in the easiest way and in a detailed way see you in the next class [Music]