Understanding Motion Through Graphs and Equations

Hey all welcome to homeschool and welcome back to class 9 chapter motion already two videos are completed on a chapter video links are provided in the description you can just go and watch it out if you have not yet watched and this is our last session on a chapter motion where I will be discussing about graphs, how to plot a graphs and what information does graphs can give and how graphs can describe about motion. All that we will discuss and then the three important equations of motion which we call it as kinematic equations and how to derive those equation from the graph and a few problems based on those equations so this is what i'm going to complete in this particular video and this topic is really the most important topic of this chapter okay so watch the video carefully video can be quite lengthy but then definitely you will have that feel of understanding after the completion of the video and don't forget to post your opinion about the video in the comments. Fine, let's start the topic. Soo, first one let's talk about graphs. Oakay, so which I normally call it as motion graphs. Oakay, so we are going to study two types of graphs, right and before we go for the types of graphs and what graphs we study. let's understand what actually we mean by a graph right so this is a common word uh we hear in a day to day life i mean if you watch tv uh for example you are watching a great cricket match uh there they will show some graphs onto a side right uh say uh the graphs will have i mean they will tell you like in which over how many runs a particular team had got you know all that if they want to analyze you know they'll plot a graph and from a graph they will come to know the information see complete information they will not come to know at least basic information they will come to know that in which over you know how many runs a particular team has secured and and that way they can compare the performance of one team with the performance of other team right Soo this way graphs are very helpful to give basic information about a particular event. Oakay, so about a particular concept, if you want some basic information, then these graphs are the best idea. Oakay, so what actually we mean by a graph, say in RNCRDc textbook, it is mentioned as, you know, graph is a convenient method. It is a convenient method to understand. to understand basic information right basic information about an event about an event or about a particular concept okay so that's what our graphs give us and we all know how to plot a graph that I think we have learned it in mathematics right so you know how the graph paper looks like and you know what is x-axis what is y-axis right so all that basic idea hope that you people know Fine. Soo, now graphs are of various types. You have bar graphs, you have line graphs. Oakay. Soo, here in our chapter, we are mainly focusing about the line graphs. Oakay. Soo, we need to study two important graphs here one is a graph of distance and time okay so distance time graph and another one is velocity time graph velocity time graph okay so about these graphs we should study something in details first let me talk about distance time graph okay or sometimes we can say it as position time graph also okay so now let's take a word as distance here so distance time graph this is what Bdut I am going to discuss initially. Fine. Soo we all very well know that a graph is something that has two axis. We mark by taking two axis. Soee if I put this horizontal line like this it means that this is x axis okay and here when i put a vertical line then this means that this is y axis right so horizontal line this is x axis and this is y axis right fine and a distance time graph is it is a graph of distance and time you Oakay, say for example, somebody have given a information for you, you know, what a particular car is there. Oakay, so this car in what time, how much distance it has covered, you know, that that information they have given, say, for example, distance and time. Dcistance, let me measure it in meters and time, let me take it in seconds. Oakay, imagine car initially has moved 2 meters in 1 second. Oakay, how many meters? 2 meters in 1 second. Again in the next second, imagine this has moved 4 meters. In the third second, imagine the car has moved 6 meters. In the fourth second, car has moved 8 meters. In the fifth second, car has moved 10 meters. Right? Soay this is what the information you know. This is the distance traveled by a car at a particular time instance. Oakay. Soo this one, you have to plot on a graph. Soo what will you do? You will just put one line horizontally, you will call it as x axis. And one line vertically, you will call it as y axis. Oakay. And now, and y axis is always distance. I consider y axis as distance. And I consider time as x axis. Always consider time as x axis. Oakay, because time is the one which does not depend on anything. Oakay, whatever may happen, time goes on, right? Soo, time is something that do not depend. Oakay, so that's why actually time is always taken in x axis. Oakay, and distance is taken in y axis. right okay so time you see the time one second two second three second four second five second so how do you take a scale so this is our zero uh let it be one second two second three second four second five second six seconds so this is how you will take a scale and coming to distance distance you see two meter four meter six meter eight meter ten meter say equal you know uh difference is there Soo just this one only you can take it as a scale. Soo it is 2 meters, right? 4 meters and 6 meters, 8 meters and so on. Oakay. Soo what is this? This is distance. Let me indicate this as small d, right? And now you see the first values, you know, the first trial you see distance at 1 second. how much was the distance covered by a car? 2 meters, right? Soo, at 1 second, 2 meters. Soo, here you will put a point, right? And where will you put the next point? At 2 seconds, the car has traveled 4 meters, right? Soo, where is 2 in the time slot? Here is 2. Where is 4? Soo, somewhere here you will mark. Then the third one, third second, 6 meters was the distance covered. Then in the fourth second, 8 meters was the distance covered. In the fifth second, 10 meters was the distance covered, right? Soo, these are what we call it as coordinate. What is the coordinate for this point? How much is the time? 1. What is the coordinate? 1, 2 we write, okay? Soo, time is 1. In the x-axis, this point is corresponding to 1. And in the y-axis, this point is corresponding to 2. Soo, 1, 2 we say as coordinates for this point. Oakay, now if I join all the points through 0, see I join all the points. Soo, this is how I get a straight line. Oakay, so this is a distance time graph for, okay, for, this is a graph for uniform motion, uniform motion. Oakay, so this is the distance time graph. for uniform motion. Remember, why I am calling this as a uniform motion? Bdecause equal distances are covered in equal instances of time, right? Soo, what is the time gap between first and second? Oane second. In one second, how much was the distance covered? Two meters. Again, you see the time gap between second and third? Oane second. In one second, how much was the distance covered? Two meters. Soay, For every second, 2 meters is the difference, is the gap covered, right? Is the distance covered? Soo, you know, equal distances are covered in equal intervals of time. Souch a motion, we will call it as uniform motion, isn't it? Soo, that's why I will call it as distance time graph for uniform motion. Soee, for... uniform motion always you will get a straight line. Always graph looks straight. Oakay. Soo, the line in a graph is always straight. For which motion? For uniform motion only. Right. Soo, always you will get straight line. Soo, this is what you need to remember. This is the first point that you need to remember. Oakay. Soo, now let me tell you what end all is the information that you can get to know from this graph okay say okay this is a uniform motion straight line you got so the moment you see a straight line you can quickly say oh equal distances are covered in equal time that's what you can say right and then what all the information that you can get you know what From distance time graph, we can calculate speed. Oakay. At a particular point, what is the speed of a vehicle? That also we can calculate. Right. Soo, what is the first point I am going to tell you? From, this is very important guys, from distance time graph, distance time graph, what we can calculate? We can calculate We can calculate speed. Oakay, speed we can calculate. Soo what is speed? What is the formula for speed? Sopeed is equal to distance by time. Isn't it? Oakay. Soee guys, if I have to find out speed at this point, okay, speed at this point, let this point be A. Oakay. Soo, what am I trying to find out? Sopeed at point A. point A. Oakay, so how can I find out? I can draw a one line like this, a dotted line perpendicular to x-axis. Oakay, so from this point, if I draw a straight line touching x-axis, this is where it meets okay and if I draw another line touching y-axis okay so this is where it meets say at this point okay can you write the coordinates of this point in the x-axis it is touching at 2 in the y-axis if I draw a line right it is touching at 4 meters so can you tell me what is the time 2 seconds. What is the distance covered by an object at this point? It is 4 meters, right? Soo, speed at point A, distance covered is how much? 4 meters. 4 divided by time is 2, right? Soo, what is your answer? Your answer is 2 meter per second. This is how you can always calculate speed of an object at a particular point. Oakay, say if you want to calculate speed at this point, what you have to do? Just draw a line perpendicular to the x axis. This is what the time at this point, this is what the time, okay, and another line on to a y axis. Soo, this is what the distance. Soo, this number divided by this number you have to do. Oakay, so this is the distance and this is what the time. Dcistance by time itself is the speed, right? Soo, this is how from the graph you can always find out the speed of an object at the particular points. Oakay, fine. Soo, this is one importance of graph. Oakay, DcT graph, Dc in the sense distance. Soecond importance is very, very important. Understand carefully. From. DcT graph, okay, let me write it as DcT graph in short. From DcT graph, we can find, we can find velocity also, okay, velocity also we can find. First, let us try to understand stand what is the formula of velocity it was displacement it is not the distance there is lots of difference between distance and displacement which was very clearly explained in my first video link is provided go and watch okay so velocity is equal to displacement by time right so now from a graph how do you find out the displacement Soay for example, let me consider this point as A and this point as Bd. And this is what the displacement. The gap between A and Bd, this much is the displacement. Soo this is the displacement. Soo how much is the displacement guys? This much. That means let me call. this point as So2 and let me call this point as So1. Oakay, so what is displacement here? So2 minus So1 divided by time. What is the time interval? This is the time, right? X axis side is time. Soo, let me call this as T2, this as T1. Oakay, so what is the time interval? T2 minus T1. Oakay, now what is So2? Soubstitute, what is So2? So2 is 8 meters and what is So1? Oakay, so displacement is this. This much is displacement. This much is time interval. I want to find out velocity between these two points. Oakay. Soo, displacement by time. Dcisplacement means change in position. Oabject was here. Now, it is here. Change in position is called displacement. Soo, how much is the displacement? These many meters. That means 8 minus 4. Oakay. How much is the time? t2 minus t1. That is 4 minus 2. Right. Soo, 8 minus 4 meters is the displacement and time is t2. t2 is how much? 4, t1 is 2, right? Soo, 8 minus 4 is 4 and 4 minus 2 is 2. Soo, 1's are, 2's are, right? Soo, what is the velocity? Vtelocity is equal to 2 meter per second, right? Soo, there is a difference, right? Soay, just try to analyze how you found the speed at the point speed at the point you considered only co-ordinates right and Soee how we found velocity. Vtelocity is nothing but displacement. Dcisplacement is always between two points. Consider any two points. I considered A and Bd. Oakay. Soo this is this gap. This gap is your displacement. This is your displacement. Oakay. And this gap is your time difference, time interval. time interval. Oakay. Soo, if this is t2 t1, t2 minus t1 you have to do. Dcisplacement to find. If this is s1, this is s2. s2 minus s1 you have to do. Oakay. Soo, velocity is always displacement by time, speed is always distance by time. Soo this is how we can calculate speed and velocity from a graph, from the information of a graph. Soo hope you understood what is the use of a graph. I mean graphs are used to describe the motion. That's what we are learning. Soee. From a graph, you can able to find speed and velocity, right? Like that, we can find many more things. Oakay, so now we have learned distance time graph for uniform motion. And we also know how to find speed of an object or velocity of an object. I mean from a graph. Soo now we will learn another type of distance time graph. okay we learnt it for uniform motion now let us see how graph looks for non-uniform motion so now guys with the given information on a board can you able to plot a graph and looking at the information can you able to say whether it is a uniform motion or non-uniform motion definitely yes you see at zero second distance traveled is zero At 2 seconds, the distance traveled is 1 meter. At 4 seconds, distance traveled is 4. What is the gap? Here, what is the gap between this and this? What is the difference between this and this? It is 2 seconds, right? Bdut what is the difference between this and this? It is, you know, Almost around 3 meters. And you know, and now you see at 6th second distance traveled is 9. At 8th second distance traveled is 16. Again, what is the difference between 9 and 16? Yes, it's more than 3, right? It's not 3. That means at equal intervals of time, the distance traveled is different. It is not same. If same distances are covered in equal amount of time like in the previous case we called it as uniform motion. Now this is an information about non-uniform motion. Oakay. Soo looking at the information you know you must able to tell whether this is uniform motion or non-uniform motion. Oakay. Equal intervals of time but equal distances are not covered. Right. okay so how do you plot a graph for this see how a graph looks so this is y axis and this is the x axis so x axis i am taking time so always time must be in x axis and distance must be in y axis so x axis is a time right so how do i take a scale this is 0 and this can be 2 4 6 8 10 12. Soo this is how you can take and how do you take distance along y axis? How do you take a scale 0 and let me take it as 5, 10, 15, 20, 25 and so on. Now try to plot a graph at 0 distance is also 0. At time 2, at time 2, what is the distance? 1. 1 in the sense somewhere here you will get a point. Right? Oakay. Soo, at 4 seconds, what is the distance? 4. That means 4 means it is below 5. Soomewhere here you will get a dot. Right? Oakay. Soo, at 6th second, what is the distance covered? It is 9 here. That means somewhere here you will get a dot. Soo at 8th second, what is the distance? 16, right? Soo where is 16? Here is 15. Soo that means somewhere here you will get a dot, right? And at 10, it is 25. At 10, it is 25. That means, you know, somewhere here you will get like that. And if you join from 0, if you join all the points, see how do you get? Dco you get a straight line like a previous case? No, you are getting a curve. right so you are getting a curve so curve is the one that you get when you plot a graph of you know distance versus time for non-uniform motion so whenever you have a curve like this okay in dt then that graph is for non-uniform motion, non-uniform motion, okay? Soo, this is really very important and you must know how a graph of uniform motion looks and a graph of non-uniform motion looks for DcT graph, okay? Soo, when you consider distance versus time, For uniform motion, you get a straight line. For your non-uniform motion, you get a curve. Soo this is really very important. And what you can always calculate from a graph? We can always calculate speed and velocity from DcT graph. Oakay, fine. And now we will go for next type of a graph, VtT graph. That is velocity time graph. Oakay. Soo coming to velocity time graph, this is one of the very very important graph that one must have idea on. Soo in short we can call it as VtT graph and many many things we can find from VtT graphs. Soee first let me plot a graph. Soo taking y-axis and x-axis, I always told you to take time in x-axis and this guy that is velocity in y-axis. Oakay. Soo, just try to observe this information guys. Imagine time. Oakay. And velocity information I am giving you and try to plot a graph here. Time in second, velocity in meter per second. Right. Oakay. Soo, time. Oakay, so let me start with okay one second. Soo at one second velocity was around the you know 20 meter per second and at Two seconds the velocity was 20 meter per second At 3 seconds also velocity was 20 meter per second. At 4th second also velocity was 20 meter per second. Soo what you can understand from this information? Oakay, so let me plot a graph here. Oakay, let me take time this is 0 and this is 1, 2, 3, 4, 5, 6 and so on. Oakay, so velocity what is the scale I can take? Oakay, let me take it 5. Oakay, 10. 15, 20 like that. Oakay. And you see here, let me plot at first second at time one, what was the velocity? 20. Soo at second second, what was the velocity of an object? 20 only. And at the third second, 20. At the fourth second also 20. At the fifth second also 20. Soo if I join all the dots, you know, this is what the line I get, right? Soay I get straight line parallel to x axis. Oakay. Soo what is this? A line. I am getting a line parallel to x axis. Isn't it? Soay what does this mean? Can you think of for which motion you get a graph like this? It is for uniform motion. Oakay. Soo for uniform motion. What is uniform motion? Equal distances in equal. instance of time, right? Oar you know for uniform motion, velocity or speed remains constant. Soo, what is this graph indicating for us? From the graph, we can say that velocity is constant, right? And velocity is constant for uniform motion. Uniform motion. Soo the graph that I mentioned on a boat, this is the graph for which motion guys, uniform motion. This is very important to understand. Oakay. Soo for uniform motion only, our speed or velocity is always constant. Soo you get a straight line. You see velocity have not changed, but the time has changed. I mean, the object is moving with the same speed at every time interval, right? Soo that's the reason you got this line, you know, parallel to x-axis. Oakay, so now from this particular graph, what is the information that you can get to know? Vtery, very important guys from this graph, from VtT graph. Oakay, so what we can find is we can find displacement. We can find displacement. This is very important or distance covered by an object. Oakay, displacement or distance covered by an object. That is what we can able to find out. Oakay, so how to find that? You know what? Let me consider two points here. Oakay, so this is point A and this is point Bd. These are the two points I am considering. Oakay, so now from A, I will draw a line perpendicular to x-axis, okay? And from Bd also, I will, okay, let me take this as a Bd, right? Oakay. Soo, from Bd, let me draw a line perpendicular to, you know, x-axis, okay? Soo, you know, this is A. Let me call this as, you know, C. Oakay, so this is A and this is C. Oakay, and now the area, this area will give you the value of displacement. Oakay, so the area covered between A, Bd, C, Dc will give you the value for displacement. This is very, very important to understand. Soo from this particular graph, we can calculate displacement. Oakay, so the area covered between A, Bd, C, Dc, you know from A, a line, perpendicular line you have drawn, right? And from Bd, you extended this point, you know, a line is drawn onto x-axis, from A, a line is drawn onto a d-axis and this area, you know, area is this area. of A, Bd, C, Dc is the value for displacement. Soo, if you can calculate the area of A, Bd, C, Dc, then that itself is the answer for displacement or distance covered by an object. Soo, what is the distance or displacement here? is equal to area area of a b c d so what is a b c d it's like a rectangle right so how do you calculate the area of rectangle it is length into breadth right it is length into breadth so you area of rectangle. It's nothing but a rectangle, right? Soo, length into breadth. Soo, what is length here? Length is dc, right? Soo, dc. This is d. dc. This much. This much is the length, right? Into breadth. Soo, how much is the breadth? What is the breadth here? ad. ADc is the breadth. Soo, what is the value of DcC? DcC, right? And it was DcC is how much? Soee, 2, 5, right? DcC is nothing but Soee, Dc is at time 2 seconds and you know C is at time 5 seconds. Soo, your DcC is equal to I can say 5 minus 2. Soo, DcC is equal to 3 seconds, right? Soo, first second, second second, third second. Soo, DcC length, this DcC value is 3 seconds. Soo how much is our ADc? ADc this is our breadth right? ADc's value is how much? Soo 0 to 20 that means you know 20 meter per second. Soo ADc value is 20 meter per second that is this much this much value and DcC is this much this difference. Soo 5 minus 2, 2 you have to do right. Soo what is our DcC? DcC is 3. into and ADc is 20, right? Soo, what is your answer? It is 60 meters. Soo, what is your distance or displacement here? Dcistance, okay, let me call here distance or displacement is one and the same in this case, okay? Soo, that is around 60 meters. Soo, this is how you can calculate distance or displacement from VtT graph. It's nothing but the area covered. Oakay. You know, this is one of the very, very important use. And now let us discuss about VtT graph for non-uniform motion. Remember, doing VtT graph for non-uniform motion. This is the graph for uniform motion. And from this, we got to know how to calculate the distance or displacement. It is just the area covered in. this particular region. Oakay fine. Soee guys observe how VtT graph of non-uniform motion looks like. Non-uniform motion. Remember here but the acceleration is uniform. Oakay, non-uniform motion with uniform acceleration. This is very very important. Acceleration is uniform only, right? We normally say it as uniformly accelerated motion. Uniformly accelerated motion. Soo, uniform in the sense what? Constant. Acceleration is constant. Sopeeding up is constant, okay? Bdut the velocity may not be constant, right? Soo, such a motion, we will call it as uniformly accelerated motion, okay? Fine. Soo, when you plot a graph, say I am directly showing you how a graph looks, okay? Soo, this is velocity in y-axis, time in x-axis, okay? let me consider time something like this 5 seconds uh you know 10 seconds 15 seconds 20 seconds 25 seconds and velocity as uh you know 10 meter per second uh 20 meter per second 30 meter per second 40 meter per second 50 meter per second and so on Oakay, so when you plot a graph, you get a straight line. This is really very important to understand. Oakay, so when you plot VtT graph for uniformly accelerated motion, you will always get a straight line. Oakay, so this is really very important. Soo how does a graph looks? We get a straight line, a straight line. For what kind of motion? Uniformly accelerated motion. Soo now finding distance or displacement. Oakay so in the previous graph also from VtT graph what is the important use of VtT graph? We can able to find the distance or displacement. Oakay so here in this graph how do you find the distance or displacement? Finding distance. Oakay from VtT. VtT graph of uniformly accelerated motion. Consider any two points. Soo let me consider this point A and this point Bd. These are the two points I am considering. Soo do you remember how did we calculate the distance or displacement from the previous graph? Just we have drawn a line. You know what? onto x-axis perpendicular to x-axis right from a align perpendicular to x-axis let me call this as a b is here right let me call this as c okay and another one perpendicular to x-axis let me call this as d okay and this area this area is what will give you Answer for distance or displacement. Isn't it? And what is this? This looks like a trapezium. We call this as what? Trapezium. Oakay. Soo, here area of trapezium is equal to distance. Oakay. Soo, how do you calculate the area of trapezium? Oar you can break this something like this. Right? Oane more line I will draw perpendicular to BdDc. Let me call it as E. And you know it is nothing but a combination of triangle and rectangle. rectangle right so this is rectangle and this is your triangle right so if you can find area of triangle and rectangle you add both of them that becomes area of ac db okay so area of trapezium what is trapezium here a b dc okay so area area of a b d c if you can calculate that one can be equal to the distance traveled by object okay distance traveled by object uh you know between point a and b right okay so now area of a b c d how you can calculate you can calculate area of triangle a b e plus area of rectangle rectangle what is the rectangle here a e d c okay so what is area of triangle area of triangle formula is half into oh length into base, okay? Soo, half into, it is nothing but half into base into length, right? plus what is area of rectangle? In the previous case, we have calculated length into breadth, length into breadth, right? Soo, here let's substitute half into base is how much? Bdase is A, okay? A is this much, A, A is A into length, length is how much? BdE, right? plus length into breadth. Soo, what is the length here? Length is C into breadth. Bdreadth is A. A, C. Oakay. Soo, if you can substitute the values of A, BdE, C and A, you will get one digit and that is equal to your distance. Oakay. Soo, this is the way of calculating displacement length. for uniformly accelerated motion from a graph. Oakay, so hope you understood the concept. And now I will be showing you two more graphs here. Soo try to find out what graphs are they? I mean, what type of motion they talk about? Oakay, see if I have y axis and x axis in the y axis, I'm taking velocity and in the x axis, I'm taking time. Imagine if I get a line something like this. Oakay, see if I get a line. Like this. This indicates that I'm talking about uniformly accelerated motion with negative velocity. Oakay. I'm talking about uniformly accelerated motion, accelerated motion with negative velocity. Negative velocity. I mean, if the speed decreases, okay. Soee here, what you can observe here, as the time increases, as the time increases, the speed or the velocity is also increasing, right? Soo, here speeding of object, you will notice. Bdut here, you see, as the time increases, what's happening? Your velocity is decreasing, right? Soo, here v is decreasing right so here v is decreasing so if velocity decreases as time increases then this is how a graph looks like okay so this is one more graph and another one is imagine if you have this is v and this is t this is also vt graph in case if you get something like this what does this indicate this indicates that non-uniformly accelerated motion. Soo for non-uniformly accelerated motion, if the acceleration is not constant, is not constant then you get a graph like this so actually if you have to understand from a graph this is how we can understand the object has started at this point okay and here the the speed increased again you see here there is a stop again the speed decreased speed increased again the speed decreased right so speed increased decreased increased decreased so the speed is not constant velocity is not constant i mean the acceleration is also not constant Oakay, so when the acceleration is not constant, then this is how the graph can look like. Oakay, so these are various VtT graphs, right, that we have studied and one major use of VtT graphs is finding displacement or distance. It's just the area covered is distance or displacement. Oakay, fine. And we have one more use. We can actually calculate acceleration also from VtT graph. Soo anyway, calculating acceleration from VtT graph, you will learn it in higher levels. Dcon't worry. Soo now this much is more than enough to know about the graphs for 9th level. Oakay. Soo now we will go for the three important equations of motion and how we can derive them in a simple way from a graph. And we also... talk about the numericals. We will discuss some numericals on those equations also. Soo coming to the last topic of the chapter, it is equations of motions. Soo they are very very important. Soo there are three equations of motion. Soo actually these equations will tell us what actually there is a relationship between velocity and time. displacement and time okay so just observe the equations the first very very equation is equal to v is equal to u plus 80 okay so second equation is s is equal to ut plus half 80 square this is really a very very important equation and the third one is v square minus u square is equal to 2 a s right and so you must be wondering what is this v u a t right so you we have used these terms before they are not actually new so here v is final velocity Oakay, so this is final velocity. After an object traveled certain distance, you know, if it is there at a point A after some distance, then velocity at that point A is final velocity. Oakay, so just remember Vt is final velocity. and u is initial velocity here. Soo, this is initial velocity and coming to a, a is acceleration. This is very very important acceleration and t is time. Oakay, time and coming to s, we have s. So is the distance or displacement. Actually, it's a displacement. Oakay, so for your level, I can call it as just distance. Oakay. Soo this is distance. Soo So is distance traveled by your object in a particular time. Soo time is T. A is acceleration with which an object has traveled. U is initial velocity. I mean when it started its journey or initial velocity always it cannot be a zero. Always it cannot be a rest point. Oakay so it's a initial velocity and Vt is final velocity. Soo this is what the meanings of these terms guys and here if you observe this equation you have a relationship between velocity and time and here you have a relationship between distance and time okay and here the relationship between I can say velocity and acceleration or distance right so here these terms are connected these ways. and now how do you derive them actually their derivation uh you know it's it's not so important because people derive these equations in different ways see they can derive it from a graph they can derive it normally normally with logical things okay actually you can derive them with certain definitions you know there are many ways of deriving these equations but one way of deriving them is from a graph Soo it is not that very important, but still I will tell you as it is mentioned in your textbooks. Oakay, so let us derive the first equation. Oakay, so let us try to derive. I am showing the derivation of which equation? This is v is equal to u plus 80. Soo this is this equation gives a relation between. Soo this is a relation between velocity and time. Vtelocity and time. Oakay, to derive this, let me consider a graph of uniformly accelerated motion. Oakay, so I am considering VtT graph, we know what do you mean by VtT graph, right? Soo VtT graph of uniformly accelerated motion okay accelerated motion so we know you get a straight line say if this is v in y axis and this is t in x axis Soo in the previous case, we got uniformly accelerated when we got a straight line. Bdut straight line is always need not be from point 0. Oakay, so a straight line can be at any point. Let me take from this point, you know, you got a straight line. Oakay, so now this is your initial velocity. The point where the object has started is initial velocity. If the object is started from 0, you would have got straight line from here. right so it is not always a zero initial velocity need not be zero always okay so it can be any value say the difference between the previous graph and this is just see i drew it from this point now i'm drawing it from certain point okay so the point where i started is my initial velocity that is u okay so let me consider this as a point a Oakay, so this is our initial velocity of an object. Fine. And let this point be Bd, right? Oakay. Soo now what I will do is I will draw a line. Oakay, so this is the extended line. Soo this is the line I draw perpendicular to y axis. I am calling it as let it be C. Oakay. And a line that I draw perpendicular to x axis and let me call this as d right maybe these things are different in your ncrt textbooks right however you want you can name them however you want okay fine Soo now what I do is okay so one more line I will draw here okay so let me call this as point you know a is over b so let me call this as e okay fine and we all very well this is point o this is point o okay so what you can understand from a graph is this distance this much this o a let o a you OaA is initial velocity. This is initial velocity. This length, this, this length, this velocity on, you know, y axis, that is your initial velocity. Oakay. Soo that is initial velocity. You always remember OaA is U. Oakay. And let BdDc or, you know, C. Oakay. This C or BdDc, right? Soo, this BdDc, if I take it on y-axis, this much is the length, okay? Soo, what is this final velocity? Oakay, so this is actually final velocity Vt. Soo, BdDc, BdDc is final velocity, final velocity Vt, okay? And see here, OaDc. OaDc is time interval. What is this gap? This is nothing but say if I consider this as t2, this is t1, t2 minus t1. That is time interval. Soo OaDc is time. It is nothing but time t. Oakay, so now if I have to derive a first equation, let me consider the definition of acceleration. Soo we studied what do you mean by acceleration? Acceleration is nothing but change in velocity, right? It is nothing but change in velocity by time. Right? Soo what is change in velocity here? What is change in velocity? It is actually BdDc that is this much, this much, this is the final velocity minus initial velocity. Final velocity is how much? Oakay, let me write it here. Change in velocity is nothing but final velocity minus initial velocity velocity right so what is final velocity final velocity is how much BdDc right so BdDc yeah divided by time Soo final velocity is BdDc. BdDc minus initial velocity. Initial velocity is OaA. Oakay. Soee it is BdDc. BdDc means this much. BdDc minus OaA. much this much is the change in velocity right so how do you get this much this minus this this minus this you will get this right so this is change in velocity this is what we calculated. Soo, how do you calculate this? This, what is this? BdDc, okay, minus TAOa or OaA, okay. Soo, BdDc minus OaA divided by time is what? Time is what? Time is OaDc, right? Time is OaDc. Time is OaDc, right? Soo, let me do it here. Soo, that's what. Soo, now acceleration, acceleration symbol is A. Soo, acceleration is equal to BdDc minus OaA divided by OaDc. What is BdDc? BdDc is Vt I told. I took BdDc as Vt. minus what is o a o a is u divided by what is o d o d is t right so now this i will bring it with a i can write a t is equal to v minus u so this u if i bring it here you know how can i rearrange v is equal to v is equal to u plus a t i got my equation okay so this is the first kinematic equation first equation of motion Vt is equal to u plus 80 so hope you understood how we derived just you know I have drawn a straight line from a Oakay? And you know I have done a perpendicular line onto x-axis and a perpendicular line onto y-axis also. Oakay? Soo what I just done is I have applied the formula of acceleration, the definition of acceleration. Acceleration is change in velocity by time. Oakay? Soo change in velocity is how much? This is find. final velocity. Oakay? Soo, this much minus this. Soo, this much is the change in velocity. How do you calculate this? This minus this right. Soo this we called it as v this o a we called it as u and this we know time interval. Soo that that's what we substituted and got the formula right. Oakay so now we will go for deriving the second formula that is s is equal to ut plus half at square. Soee guys derivation of s is equal to ut plus half at square. This is the relationship relationship between position and time okay so here s is actually distance from the same graph i can derive it easily yes is what i told s is nothing but distance right and do you remember in the previous i mean just a few minutes before we have learned how to find distance or displacement from vt graph it's nothing but the area covered right so here This area covered. Soo this is the area covered between A and Bd. Bdetween A and Bd, how much is the area covered? This is the area covered. Oakay. Soo the area of Oa, A, Bd, Dc will give you the answer for distance. Oakay. What is yes here? Yes, that is nothing but distance. Is area enclosed, area enclosed or area covered in OaADc. OaADc. Oakay, so this much is the area enclosed. so what is this what is this o a b d is nothing but trapezium right so trapezium is again nothing but what trapezium is nothing but what it is it is this triangle plus this rectangle Oakay, so here OaADc is equal to what is that triangle A plus rectangle plus a rectangle o a e d okay o a e d okay so this is area of this area of o a b is nothing but area of triangle plus area of rectangle right okay so now area of oabd area of oabd is nothing but what yes right so s is equal to area of triangle area of triangle is what it is base into height what is base ye right into height. Height is BdE. Right? Soo BdE. Oakay? A into BdE. Oakay. And now plus area of rectangle is how much? Rectangle OaA DcE. Length into breadth. Soo what is the breadth? OaA. OaA is the breadth of the rectangle. Oakay? Into? Length. Length is how much? OaDc. Right? Oakay. Soo, So is equal to A is what? A. A is nothing but OaDc. Yes? OaDc is nothing but time interval. Oakay? OaDc is nothing but time interval. Right? Soo, A E is equal to OaDc. OaDc is equal to T. Soo, I will write T here into BdE. Oakay. Let me discuss BdE. Let me write it as BdE as of now plus OaA. What is OaA? OaA is initial velocity, right? OaA is this much. This is nothing but initial velocity U. Oakay. Into OaDc. OaDcE is what? Time interval, time interval, time gap. Soo that is T. Oakay, fine. Soo now we want the value of Bd. Oakay, let me write that equation here. So is equal to T into BdE, right? Plus UT. Soo we want to know what What is BdE here? Right? Oakay. Soo let's understand what do you mean by BdE? Soay actually speaking from VtT graph. From VtT graph, we can calculate, we can calculate acceleration. What is that? We can calculate acceleration. Oakay. Soo, you know, what do you mean by acceleration? How do we calculate acceleration? Acceleration is nothing but change in velocity, right? Soo, it is nothing but change in velocity. by time. Yes? Oakay. Soo, now what is change in velocity here that is from the graph? Soee, this much. This much is, this is initial velocity, this is final velocity. This much is the change in velocity that is A. Oaur A is equal to BdE, no? A, see this length is equal to BdE, right? Soo, here in case of change in velocity, I will write it as BdE, right? Soo, BdE and divided by time, okay? Time, let it be T. Soo, that means, can I write BdE is equal to A? Dcefinitely. Soo, our BdE is equal to A. right? Soo, what I will write here So is equal to T E into Bd A is nothing but what? A T, right? A T plus U T. Soo, what do I get? So is equal to A T square plus U T. That's what this I can also write it as So is equal to U T plus guys what we have forgot here area of triangle is actually half into half into base into height right so everywhere half we forgot so there comes half and here comes half right so here also comes half so what i can write here s is equal to ut plus half at square so somehow such mistakes are made right so everywhere we have to include that half Soo this is how we can derive So is equal to U T plus half A T square. Right. Soo hope you understood the derivation. Anyway derivation is not that important. Remembering the equation is important. Soo if you go for a higher level you will see that this equation is being derived from another means. Oakay. Soo by another concept. Soo as of now since it's mentioned in a textbook we are just deriving. And now let me derive the third equation. Soay third equation I will derive it in a much simple way that is not from a graph. Just observe how do I derive a third equation. Soee guys observe carefully the derivation of this equation. Soee it's very simple if you go in this way right. Soo we all know average velocity formula right. Average velocity formula we learnt in case of velocity. It is nothing but v plus u divided by 2. It's called average velocity. Initial velocity, final velocity divided by 2 for uniform accelerated motion. Oakay. Soo now velocity v. is what? The definition of velocity is what? We all know it is displacement. Vtelocity definition. Instead of writing average velocity word, I am writing its definition. Dcisplacement divided by type, right, is equal to v plus u by 2. What is displacement? Dcisplacement symbol is yes, or distance or displacement is one and the same in this case. Yes by t is equal to v plus u by 2. Soo, here s is equal to what I can write v plus u by 2 into t. Oakay, and I will shift this 2 here. Soo, I will write it as 2s is equal to v plus u into t. Oakay, so let me call this equation as 1. Oakay, fine. And we know the equation, we know the first equation, what is that? v is equal to u plus at, right? I will shift this u this side. Soo, v minus u is equal to at, I can write, right? Soo, here I can write a is equal to v minus u by t right. Soo the same equation I can write it in this way this is equation 2. Oakay, so multiplying equation 1 and 2, what do you get? Multiply LHSo, Lhs. This is LHSo, this is Lhs. This is LHSo, this is Lhs. Multiply LHSo with LHSo. Soo, 2So into A. Multiply Lhs with Lhs. How do you multiply? v plus u into t into this one. v minus u by t. Soo, this t gets cancelled. Soo, what is remaining? u v plus u. v minus u. Soo, what do you get? v into v. v square and the v into u. Soo let me write it as minus VtU plus U into Vt, U, right? U plus U into minus U. That will be minus U square. This minus U plus U gets cancelled. Soo what do you get guys? 2 A s is equal to v square minus u square, right? Soo, this is your equation, right? Soo, very simple. Soo, this we know. Actually, from graph, this is what we will come to know. From graph, okay so the distance how do you find it is the you know area of trapezium so when you take it from graph also this is the equation you will get and we know this equation on multiplying both of them we get the final equation this okay so it's very simple so we have discussed the derivation of all three equations and now we will see few important problems like how we can solve a problem if a question is asked okay Soo depending on all the equations we can solve a question. Soo let's see few numericals or problems that we have in our chapter. Look at the question number one guys. A train starting from rest attains a velocity of 72 kilometer per hour in five minutes. Oakay so there is a train right and it was at rest it was at rest in the sense u is equal to 0 meter per second what is u initial velocity and it traveled for about 5 minutes and it is somewhere here right and this is the final position so the final velocity of a train is 72 kilometer per hour What they asked you to find out? Acceleration. Oakay, so u is equal to 0 meter per second. Time is 5 minutes. Oakay, and this one velocity is 72 kilometer per hour. Convert this into meter per second. 72, right? Soo 1 kilometer is equal to 1000 meters, right? Soo 72 kilometers is how many meters? It is 1000. Soee 72 kilometers. K, small k means 1000 divided by hour. Soo 1 hour is equal to 3600 seconds. Soo 3600, okay? Soo if you do this calculation, how much do you get? 720 divided by 36. It is almost 20 meter per second. Soo this is your Vt. Oakay. Soo Vt is this much, U is this much. Time is 5 minutes. Now convert it into seconds. Soo T is equal to 5 into 60. Soo 5, 6 are 30. Soo what? 300 seconds. Soo time must be in seconds, velocity must be in meter per seconds. Soo you have to first convert that if it is there in minutes and if it is there in kilometer per hour. This is really very important. Soo now you calculate acceleration. Soo what is the formula? Vt is equal to u plus a t. Right. Soo v minus u divided by t is equal to acceleration. Right. Soo what is v? It is 20 minus u is 0 divided by time is 300. Right. Soo is equal to a. Soo what do you get? 20 divided by 300. This get cancelled. 1sr, 2 1sr, 2 5sr is equal to a. Soo a is equal to 1 by 15 meter per second square is the unit. Soo this is the answer for first question. And coming to second question, what is the second question? Dcistance traveled by a train. Whenever they asked about distance, right? You can use the formula So is equal to U T plus half A T square. Oakay. Soo here U is 0 into time is 300 seconds. plus half into acceleration is how much just now you calculated it is 1 by 15 into times square that is 300 square right so s is equal to 0 into something 0 plus 1 by this 2 into 15 if you do how much do you get 2 5s are 10, 2 1s are 2, 3. Soo it is 30 into 300 square that is 300 into 300 you have to do. Right. Soo 1 0 cancel with 1 0. Soo this is 1s are 1 0. right? 3 ones are 1, 0. Soo, 300 into 10, how much do you get? So is equal to 3000 meters or So is equal to 3 kilometer, okay? 1 kilometer is 1000 meters, no? Soo, 3000 meters is 3 kilometers, okay? Soo, this is how you will solve the problem. Vtery simple, right? Bdut converting is very, very important. There you have to be careful. Coming to second problem, very very important. Soee here, the brakes applied to a car produce acceleration 6 meter per second square in opposite direction of motion. If car takes 2 seconds to stop, calculate distance it travels during this time. Soee there is a car, right? Oakay, and this car is moving and suddenly you applied brakes, okay? Souddenly you applied brakes. And you know, soon after applying brake, it will not stop, right? It will move to a certain distance, right? Soo, it moved to a certain distance and it stopped. Oakay. Soo, how much is the time took place for a car to move from here to here? It is 2 seconds. That is the time. And what is the distance? This distance they are asking you to calculate. Oakay. Soo, here. Acceleration you see acceleration is given 6 meter per second square but the acceleration in opposite direction if at all if they mention acceleration in opposite direction then a sign should be minus. A has a sign, Vt has a sign, U has a sign. Oakay so here you have to be careful. Soay if something is there in opposite direction then sign have to be negative. Soo here a value should be minus 6 meter per second square. Oakay so now how do you calculate? They asked you to calculate distance right. Dcistance when they asked you always use the formula s is equal to ut plus half at square. Soee here initial velocity is not given you have to calculate. Oakay see final velocity is how much? Soee after some distance car stops. Soo final velocity, velocity of a car when it is stopped. Soo v is equal to 0. Oakay, a is equal to minus 6 meter per second square. Soo what is u guys? Soo calculate u now. We know the formula v is equal to u plus 80. Right? Soo it is v minus 80 is equal to u. Soo your Vt is how much? 0 minus A is how much? Minus 6 into T is 2 seconds. Time is 2 seconds. Oakay. Soo your U is equal to 12 meter per second. Isn't it? Soo that U value you substitute here. Soo U is 12 into time is 2 seconds plus half A is minus 6 into t square is 2 square. Soo, here this will be 24, right, plus half into minus 6 into 4. Soo 2 1s are 2 2s are right. Soo 24 minus into plus minus 6 2s are 12. Soo So is equal to 12 meters is the answer. Soo that's all about the problem guys. Soo here when you take a sign for acceleration you have to be very very careful. When they mention something if the acceleration is acted in opposite direction. then definitely a value must be minus okay so these are two examples and likewise the more examples you solve the more perfect you will become so apply the formulas just read the question properly try to understand if you can put one figure you feel it much easy what is given and what is that you have to calculate no your analyzation becomes easy when you put the figure Soo, use the formulas and calculate various numericals. With this, I am completing this chapter. Motion. Oakay. Soo, hope you enjoyed the concept. If you have understood, just post your opinion in the comments and meet you up with the next chapter. Soee you. Dco subscribe our channel to learn the concepts in the easiest way and in a detailed way. Thank you.

Soo, first one let's talk about graphs. Oakay, so which I normally call it as motion graphs. Oakay, so we are going to study two types of graphs, right and before we go for the types of graphs and what graphs we study. let's understand what actually we mean by a graph right so this is a common word uh we hear in a day to day life i mean if you watch tv uh for example you are watching a great cricket match uh there they will show some graphs onto a side right uh say uh the graphs will have i mean they will tell you like in which over how many runs a particular team had got you know all that if they want to analyze you know they'll plot a graph and from a graph they will come to know the information see complete information they will not come to know at least basic information they will come to know that in which over you know how many runs a particular team has secured and and that way they can compare the performance of one team with the performance of other team right Soo this way graphs are very helpful to give basic information about a particular event.

Oakay, so about a particular concept, if you want some basic information, then these graphs are the best idea. Oakay, so what actually we mean by a graph, say in RNCRDc textbook, it is mentioned as, you know, graph is a convenient method. It is a convenient method to understand. to understand basic information right basic information about an event about an event or about a particular concept okay so that's what our graphs give us and we all know how to plot a graph that I think we have learned it in mathematics right so you know how the graph paper looks like and you know what is x-axis what is y-axis right so all that basic idea hope that you people know Fine. Soo, now graphs are of various types.

You have bar graphs, you have line graphs. Oakay. Soo, here in our chapter, we are mainly focusing about the line graphs.

Oakay. Soo, we need to study two important graphs here one is a graph of distance and time okay so distance time graph and another one is velocity time graph velocity time graph okay so about these graphs we should study something in details first let me talk about distance time graph okay or sometimes we can say it as position time graph also okay so now let's take a word as distance here so distance time graph this is what Bdut I am going to discuss initially. Fine.

Soo we all very well know that a graph is something that has two axis. We mark by taking two axis. Soee if I put this horizontal line like this it means that this is x axis okay and here when i put a vertical line then this means that this is y axis right so horizontal line this is x axis and this is y axis right fine and a distance time graph is it is a graph of distance and time you Oakay, say for example, somebody have given a information for you, you know, what a particular car is there.

Oakay, so this car in what time, how much distance it has covered, you know, that that information they have given, say, for example, distance and time. Dcistance, let me measure it in meters and time, let me take it in seconds. Oakay, imagine car initially has moved 2 meters in 1 second.

Oakay, how many meters? 2 meters in 1 second. Again in the next second, imagine this has moved 4 meters. In the third second, imagine the car has moved 6 meters. In the fourth second, car has moved 8 meters.

In the fifth second, car has moved 10 meters. Right? Soay this is what the information you know. This is the distance traveled by a car at a particular time instance.

Oakay. Soo this one, you have to plot on a graph. Soo what will you do?

You will just put one line horizontally, you will call it as x axis. And one line vertically, you will call it as y axis. Oakay. And now, and y axis is always distance.

I consider y axis as distance. And I consider time as x axis. Always consider time as x axis.

Oakay, because time is the one which does not depend on anything. Oakay, whatever may happen, time goes on, right? Soo, time is something that do not depend. Oakay, so that's why actually time is always taken in x axis. Oakay, and distance is taken in y axis.

right okay so time you see the time one second two second three second four second five second so how do you take a scale so this is our zero uh let it be one second two second three second four second five second six seconds so this is how you will take a scale and coming to distance distance you see two meter four meter six meter eight meter ten meter say equal you know uh difference is there Soo just this one only you can take it as a scale. Soo it is 2 meters, right? 4 meters and 6 meters, 8 meters and so on.

Oakay. Soo what is this? This is distance.

Let me indicate this as small d, right? And now you see the first values, you know, the first trial you see distance at 1 second. how much was the distance covered by a car? 2 meters, right?

Soo, at 1 second, 2 meters. Soo, here you will put a point, right? And where will you put the next point?

At 2 seconds, the car has traveled 4 meters, right? Soo, where is 2 in the time slot? Here is 2. Where is 4?

Soo, somewhere here you will mark. Then the third one, third second, 6 meters was the distance covered. Then in the fourth second, 8 meters was the distance covered. In the fifth second, 10 meters was the distance covered, right?

Soo, these are what we call it as coordinate. What is the coordinate for this point? How much is the time?

1. What is the coordinate? 1, 2 we write, okay? Soo, time is 1. In the x-axis, this point is corresponding to 1. And in the y-axis, this point is corresponding to 2. Soo, 1, 2 we say as coordinates for this point.

Oakay, now if I join all the points through 0, see I join all the points. Soo, this is how I get a straight line. Oakay, so this is a distance time graph for, okay, for, this is a graph for uniform motion, uniform motion.

Oakay, so this is the distance time graph. for uniform motion. Remember, why I am calling this as a uniform motion?

Bdecause equal distances are covered in equal instances of time, right? Soo, what is the time gap between first and second? Oane second.

In one second, how much was the distance covered? Two meters. Again, you see the time gap between second and third?

Oane second. In one second, how much was the distance covered? Two meters. Soay, For every second, 2 meters is the difference, is the gap covered, right? Is the distance covered?

Soo, you know, equal distances are covered in equal intervals of time. Souch a motion, we will call it as uniform motion, isn't it? Soo, that's why I will call it as distance time graph for uniform motion.

Soee, for... uniform motion always you will get a straight line. Always graph looks straight.

Oakay. Soo, the line in a graph is always straight. For which motion?

For uniform motion only. Right. Soo, always you will get straight line. Soo, this is what you need to remember. This is the first point that you need to remember.

Oakay. Soo, now let me tell you what end all is the information that you can get to know from this graph okay say okay this is a uniform motion straight line you got so the moment you see a straight line you can quickly say oh equal distances are covered in equal time that's what you can say right and then what all the information that you can get you know what From distance time graph, we can calculate speed. Oakay. At a particular point, what is the speed of a vehicle? That also we can calculate.

Right. Soo, what is the first point I am going to tell you? From, this is very important guys, from distance time graph, distance time graph, what we can calculate? We can calculate We can calculate speed. Oakay, speed we can calculate.

Soo what is speed? What is the formula for speed? Sopeed is equal to distance by time.

Isn't it? Oakay. Soee guys, if I have to find out speed at this point, okay, speed at this point, let this point be A.

Oakay. Soo, what am I trying to find out? Sopeed at point A.

point A. Oakay, so how can I find out? I can draw a one line like this, a dotted line perpendicular to x-axis.

Oakay, so from this point, if I draw a straight line touching x-axis, this is where it meets okay and if I draw another line touching y-axis okay so this is where it meets say at this point okay can you write the coordinates of this point in the x-axis it is touching at 2 in the y-axis if I draw a line right it is touching at 4 meters so can you tell me what is the time 2 seconds. What is the distance covered by an object at this point? It is 4 meters, right? Soo, speed at point A, distance covered is how much? 4 meters.

4 divided by time is 2, right? Soo, what is your answer? Your answer is 2 meter per second.

This is how you can always calculate speed of an object at a particular point. Oakay, say if you want to calculate speed at this point, what you have to do? Just draw a line perpendicular to the x axis.

This is what the time at this point, this is what the time, okay, and another line on to a y axis. Soo, this is what the distance. Soo, this number divided by this number you have to do.

Oakay, so this is the distance and this is what the time. Dcistance by time itself is the speed, right? Soo, this is how from the graph you can always find out the speed of an object at the particular points. Oakay, fine. Soo, this is one importance of graph.

Oakay, DcT graph, Dc in the sense distance. Soecond importance is very, very important. Understand carefully. From. DcT graph, okay, let me write it as DcT graph in short.

From DcT graph, we can find, we can find velocity also, okay, velocity also we can find. First, let us try to understand stand what is the formula of velocity it was displacement it is not the distance there is lots of difference between distance and displacement which was very clearly explained in my first video link is provided go and watch okay so velocity is equal to displacement by time right so now from a graph how do you find out the displacement Soay for example, let me consider this point as A and this point as Bd. And this is what the displacement.

The gap between A and Bd, this much is the displacement. Soo this is the displacement. Soo how much is the displacement guys? This much.

That means let me call. this point as So2 and let me call this point as So1. Oakay, so what is displacement here?

So2 minus So1 divided by time. What is the time interval? This is the time, right?

X axis side is time. Soo, let me call this as T2, this as T1. Oakay, so what is the time interval?

T2 minus T1. Oakay, now what is So2? Soubstitute, what is So2? So2 is 8 meters and what is So1? Oakay, so displacement is this.

This much is displacement. This much is time interval. I want to find out velocity between these two points. Oakay.

Soo, displacement by time. Dcisplacement means change in position. Oabject was here.

Now, it is here. Change in position is called displacement. Soo, how much is the displacement?

These many meters. That means 8 minus 4. Oakay. How much is the time?

t2 minus t1. That is 4 minus 2. Right. Soo, 8 minus 4 meters is the displacement and time is t2.

t2 is how much? 4, t1 is 2, right? Soo, 8 minus 4 is 4 and 4 minus 2 is 2. Soo, 1's are, 2's are, right? Soo, what is the velocity?

Vtelocity is equal to 2 meter per second, right? Soo, there is a difference, right? Soay, just try to analyze how you found the speed at the point speed at the point you considered only co-ordinates right and Soee how we found velocity. Vtelocity is nothing but displacement.

Dcisplacement is always between two points. Consider any two points. I considered A and Bd.

Oakay. Soo this is this gap. This gap is your displacement.

This is your displacement. Oakay. And this gap is your time difference, time interval.

time interval. Oakay. Soo, if this is t2 t1, t2 minus t1 you have to do.

Dcisplacement to find. If this is s1, this is s2. s2 minus s1 you have to do. Oakay.

Soo, velocity is always displacement by time, speed is always distance by time. Soo this is how we can calculate speed and velocity from a graph, from the information of a graph. Soo hope you understood what is the use of a graph.

I mean graphs are used to describe the motion. That's what we are learning. Soee. From a graph, you can able to find speed and velocity, right? Like that, we can find many more things.

Oakay, so now we have learned distance time graph for uniform motion. And we also know how to find speed of an object or velocity of an object. I mean from a graph. Soo now we will learn another type of distance time graph.

okay we learnt it for uniform motion now let us see how graph looks for non-uniform motion so now guys with the given information on a board can you able to plot a graph and looking at the information can you able to say whether it is a uniform motion or non-uniform motion definitely yes you see at zero second distance traveled is zero At 2 seconds, the distance traveled is 1 meter. At 4 seconds, distance traveled is 4. What is the gap? Here, what is the gap between this and this? What is the difference between this and this?

It is 2 seconds, right? Bdut what is the difference between this and this? It is, you know, Almost around 3 meters.

And you know, and now you see at 6th second distance traveled is 9. At 8th second distance traveled is 16. Again, what is the difference between 9 and 16? Yes, it's more than 3, right? It's not 3. That means at equal intervals of time, the distance traveled is different. It is not same.

If same distances are covered in equal amount of time like in the previous case we called it as uniform motion. Now this is an information about non-uniform motion. Oakay. Soo looking at the information you know you must able to tell whether this is uniform motion or non-uniform motion. Oakay.

Equal intervals of time but equal distances are not covered. Right. okay so how do you plot a graph for this see how a graph looks so this is y axis and this is the x axis so x axis i am taking time so always time must be in x axis and distance must be in y axis so x axis is a time right so how do i take a scale this is 0 and this can be 2 4 6 8 10 12. Soo this is how you can take and how do you take distance along y axis? How do you take a scale 0 and let me take it as 5, 10, 15, 20, 25 and so on.

Now try to plot a graph at 0 distance is also 0. At time 2, at time 2, what is the distance? 1. 1 in the sense somewhere here you will get a point. Right? Oakay. Soo, at 4 seconds, what is the distance?

4. That means 4 means it is below 5. Soomewhere here you will get a dot. Right? Oakay. Soo, at 6th second, what is the distance covered?

It is 9 here. That means somewhere here you will get a dot. Soo at 8th second, what is the distance?

16, right? Soo where is 16? Here is 15. Soo that means somewhere here you will get a dot, right? And at 10, it is 25. At 10, it is 25. That means, you know, somewhere here you will get like that.

And if you join from 0, if you join all the points, see how do you get? Dco you get a straight line like a previous case? No, you are getting a curve. right so you are getting a curve so curve is the one that you get when you plot a graph of you know distance versus time for non-uniform motion so whenever you have a curve like this okay in dt then that graph is for non-uniform motion, non-uniform motion, okay?

Soo, this is really very important and you must know how a graph of uniform motion looks and a graph of non-uniform motion looks for DcT graph, okay? Soo, when you consider distance versus time, For uniform motion, you get a straight line. For your non-uniform motion, you get a curve.

Soo this is really very important. And what you can always calculate from a graph? We can always calculate speed and velocity from DcT graph.

Oakay, fine. And now we will go for next type of a graph, VtT graph. That is velocity time graph.

Oakay. Soo coming to velocity time graph, this is one of the very very important graph that one must have idea on. Soo in short we can call it as VtT graph and many many things we can find from VtT graphs. Soee first let me plot a graph.

Soo taking y-axis and x-axis, I always told you to take time in x-axis and this guy that is velocity in y-axis. Oakay. Soo, just try to observe this information guys.

Imagine time. Oakay. And velocity information I am giving you and try to plot a graph here.

Time in second, velocity in meter per second. Right. Oakay.

Soo, time. Oakay, so let me start with okay one second. Soo at one second velocity was around the you know 20 meter per second and at Two seconds the velocity was 20 meter per second At 3 seconds also velocity was 20 meter per second. At 4th second also velocity was 20 meter per second.

Soo what you can understand from this information? Oakay, so let me plot a graph here. Oakay, let me take time this is 0 and this is 1, 2, 3, 4, 5, 6 and so on. Oakay, so velocity what is the scale I can take? Oakay, let me take it 5. Oakay, 10. 15, 20 like that.

Oakay. And you see here, let me plot at first second at time one, what was the velocity? 20. Soo at second second, what was the velocity of an object? 20 only. And at the third second, 20. At the fourth second also 20. At the fifth second also 20. Soo if I join all the dots, you know, this is what the line I get, right?

Soay I get straight line parallel to x axis. Oakay. Soo what is this? A line.

I am getting a line parallel to x axis. Isn't it? Soay what does this mean? Can you think of for which motion you get a graph like this? It is for uniform motion.

Oakay. Soo for uniform motion. What is uniform motion? Equal distances in equal. instance of time, right?

Oar you know for uniform motion, velocity or speed remains constant. Soo, what is this graph indicating for us? From the graph, we can say that velocity is constant, right? And velocity is constant for uniform motion. Uniform motion.

Soo the graph that I mentioned on a boat, this is the graph for which motion guys, uniform motion. This is very important to understand. Oakay. Soo for uniform motion only, our speed or velocity is always constant. Soo you get a straight line.

You see velocity have not changed, but the time has changed. I mean, the object is moving with the same speed at every time interval, right? Soo that's the reason you got this line, you know, parallel to x-axis.

Oakay, so now from this particular graph, what is the information that you can get to know? Vtery, very important guys from this graph, from VtT graph. Oakay, so what we can find is we can find displacement. We can find displacement. This is very important or distance covered by an object.

Oakay, displacement or distance covered by an object. That is what we can able to find out. Oakay, so how to find that?

You know what? Let me consider two points here. Oakay, so this is point A and this is point Bd. These are the two points I am considering.

Oakay, so now from A, I will draw a line perpendicular to x-axis, okay? And from Bd also, I will, okay, let me take this as a Bd, right? Oakay. Soo, from Bd, let me draw a line perpendicular to, you know, x-axis, okay? Soo, you know, this is A.

Let me call this as, you know, C. Oakay, so this is A and this is C. Oakay, and now the area, this area will give you the value of displacement. Oakay, so the area covered between A, Bd, C, Dc will give you the value for displacement. This is very, very important to understand.

Soo from this particular graph, we can calculate displacement. Oakay, so the area covered between A, Bd, C, Dc, you know from A, a line, perpendicular line you have drawn, right? And from Bd, you extended this point, you know, a line is drawn onto x-axis, from A, a line is drawn onto a d-axis and this area, you know, area is this area. of A, Bd, C, Dc is the value for displacement. Soo, if you can calculate the area of A, Bd, C, Dc, then that itself is the answer for displacement or distance covered by an object.

Soo, what is the distance or displacement here? is equal to area area of a b c d so what is a b c d it's like a rectangle right so how do you calculate the area of rectangle it is length into breadth right it is length into breadth so you area of rectangle. It's nothing but a rectangle, right?

Soo, length into breadth. Soo, what is length here? Length is dc, right?

Soo, dc. This is d. dc. This much. This much is the length, right?

Into breadth. Soo, how much is the breadth? What is the breadth here?

ad. ADc is the breadth. Soo, what is the value of DcC?

DcC, right? And it was DcC is how much? Soee, 2, 5, right?

DcC is nothing but Soee, Dc is at time 2 seconds and you know C is at time 5 seconds. Soo, your DcC is equal to I can say 5 minus 2. Soo, DcC is equal to 3 seconds, right? Soo, first second, second second, third second. Soo, DcC length, this DcC value is 3 seconds. Soo how much is our ADc?

ADc this is our breadth right? ADc's value is how much? Soo 0 to 20 that means you know 20 meter per second. Soo ADc value is 20 meter per second that is this much this much value and DcC is this much this difference. Soo 5 minus 2, 2 you have to do right.

Soo what is our DcC? DcC is 3. into and ADc is 20, right? Soo, what is your answer?

It is 60 meters. Soo, what is your distance or displacement here? Dcistance, okay, let me call here distance or displacement is one and the same in this case, okay?

Soo, that is around 60 meters. Soo, this is how you can calculate distance or displacement from VtT graph. It's nothing but the area covered.

Oakay. You know, this is one of the very, very important use. And now let us discuss about VtT graph for non-uniform motion. Remember, doing VtT graph for non-uniform motion. This is the graph for uniform motion.

And from this, we got to know how to calculate the distance or displacement. It is just the area covered in. this particular region. Oakay fine.

Soee guys observe how VtT graph of non-uniform motion looks like. Non-uniform motion. Remember here but the acceleration is uniform.

Oakay, non-uniform motion with uniform acceleration. This is very very important. Acceleration is uniform only, right?

We normally say it as uniformly accelerated motion. Uniformly accelerated motion. Soo, uniform in the sense what? Constant.

Acceleration is constant. Sopeeding up is constant, okay? Bdut the velocity may not be constant, right?

Soo, such a motion, we will call it as uniformly accelerated motion, okay? Fine. Soo, when you plot a graph, say I am directly showing you how a graph looks, okay?

Soo, this is velocity in y-axis, time in x-axis, okay? let me consider time something like this 5 seconds uh you know 10 seconds 15 seconds 20 seconds 25 seconds and velocity as uh you know 10 meter per second uh 20 meter per second 30 meter per second 40 meter per second 50 meter per second and so on Oakay, so when you plot a graph, you get a straight line. This is really very important to understand. Oakay, so when you plot VtT graph for uniformly accelerated motion, you will always get a straight line.

Oakay, so this is really very important. Soo how does a graph looks? We get a straight line, a straight line. For what kind of motion?

Uniformly accelerated motion. Soo now finding distance or displacement. Oakay so in the previous graph also from VtT graph what is the important use of VtT graph? We can able to find the distance or displacement.

Oakay so here in this graph how do you find the distance or displacement? Finding distance. Oakay from VtT.

VtT graph of uniformly accelerated motion. Consider any two points. Soo let me consider this point A and this point Bd.

These are the two points I am considering. Soo do you remember how did we calculate the distance or displacement from the previous graph? Just we have drawn a line.

You know what? onto x-axis perpendicular to x-axis right from a align perpendicular to x-axis let me call this as a b is here right let me call this as c okay and another one perpendicular to x-axis let me call this as d okay and this area this area is what will give you Answer for distance or displacement. Isn't it? And what is this?

This looks like a trapezium. We call this as what? Trapezium. Oakay. Soo, here area of trapezium is equal to distance.

Oakay. Soo, how do you calculate the area of trapezium? Oar you can break this something like this.

Right? Oane more line I will draw perpendicular to BdDc. Let me call it as E. And you know it is nothing but a combination of triangle and rectangle. rectangle right so this is rectangle and this is your triangle right so if you can find area of triangle and rectangle you add both of them that becomes area of ac db okay so area of trapezium what is trapezium here a b dc okay so area area of a b d c if you can calculate that one can be equal to the distance traveled by object okay distance traveled by object uh you know between point a and b right okay so now area of a b c d how you can calculate you can calculate area of triangle a b e plus area of rectangle rectangle what is the rectangle here a e d c okay so what is area of triangle area of triangle formula is half into oh length into base, okay?

Soo, half into, it is nothing but half into base into length, right? plus what is area of rectangle? In the previous case, we have calculated length into breadth, length into breadth, right?

Soo, here let's substitute half into base is how much? Bdase is A, okay? A is this much, A, A is A into length, length is how much? BdE, right?

plus length into breadth. Soo, what is the length here? Length is C into breadth. Bdreadth is A.

A, C. Oakay. Soo, if you can substitute the values of A, BdE, C and A, you will get one digit and that is equal to your distance. Oakay. Soo, this is the way of calculating displacement length.

for uniformly accelerated motion from a graph. Oakay, so hope you understood the concept. And now I will be showing you two more graphs here. Soo try to find out what graphs are they?

I mean, what type of motion they talk about? Oakay, see if I have y axis and x axis in the y axis, I'm taking velocity and in the x axis, I'm taking time. Imagine if I get a line something like this.

Oakay, see if I get a line. Like this. This indicates that I'm talking about uniformly accelerated motion with negative velocity. Oakay.

I'm talking about uniformly accelerated motion, accelerated motion with negative velocity. Negative velocity. I mean, if the speed decreases, okay. Soee here, what you can observe here, as the time increases, as the time increases, the speed or the velocity is also increasing, right? Soo, here speeding of object, you will notice.

Bdut here, you see, as the time increases, what's happening? Your velocity is decreasing, right? Soo, here v is decreasing right so here v is decreasing so if velocity decreases as time increases then this is how a graph looks like okay so this is one more graph and another one is imagine if you have this is v and this is t this is also vt graph in case if you get something like this what does this indicate this indicates that non-uniformly accelerated motion.

Soo for non-uniformly accelerated motion, if the acceleration is not constant, is not constant then you get a graph like this so actually if you have to understand from a graph this is how we can understand the object has started at this point okay and here the the speed increased again you see here there is a stop again the speed decreased speed increased again the speed decreased right so speed increased decreased increased decreased so the speed is not constant velocity is not constant i mean the acceleration is also not constant Oakay, so when the acceleration is not constant, then this is how the graph can look like. Oakay, so these are various VtT graphs, right, that we have studied and one major use of VtT graphs is finding displacement or distance. It's just the area covered is distance or displacement.

Oakay, fine. And we have one more use. We can actually calculate acceleration also from VtT graph.

Soo anyway, calculating acceleration from VtT graph, you will learn it in higher levels. Dcon't worry. Soo now this much is more than enough to know about the graphs for 9th level.

Oakay. Soo now we will go for the three important equations of motion and how we can derive them in a simple way from a graph. And we also...

talk about the numericals. We will discuss some numericals on those equations also. Soo coming to the last topic of the chapter, it is equations of motions. Soo they are very very important.

Soo there are three equations of motion. Soo actually these equations will tell us what actually there is a relationship between velocity and time. displacement and time okay so just observe the equations the first very very equation is equal to v is equal to u plus 80 okay so second equation is s is equal to ut plus half 80 square this is really a very very important equation and the third one is v square minus u square is equal to 2 a s right and so you must be wondering what is this v u a t right so you we have used these terms before they are not actually new so here v is final velocity Oakay, so this is final velocity.

After an object traveled certain distance, you know, if it is there at a point A after some distance, then velocity at that point A is final velocity. Oakay, so just remember Vt is final velocity. and u is initial velocity here.

Soo, this is initial velocity and coming to a, a is acceleration. This is very very important acceleration and t is time. Oakay, time and coming to s, we have s. So is the distance or displacement. Actually, it's a displacement.

Oakay, so for your level, I can call it as just distance. Oakay. Soo this is distance.

Soo So is distance traveled by your object in a particular time. Soo time is T. A is acceleration with which an object has traveled. U is initial velocity.

I mean when it started its journey or initial velocity always it cannot be a zero. Always it cannot be a rest point. Oakay so it's a initial velocity and Vt is final velocity. Soo this is what the meanings of these terms guys and here if you observe this equation you have a relationship between velocity and time and here you have a relationship between distance and time okay and here the relationship between I can say velocity and acceleration or distance right so here these terms are connected these ways. and now how do you derive them actually their derivation uh you know it's it's not so important because people derive these equations in different ways see they can derive it from a graph they can derive it normally normally with logical things okay actually you can derive them with certain definitions you know there are many ways of deriving these equations but one way of deriving them is from a graph Soo it is not that very important, but still I will tell you as it is mentioned in your textbooks.

Oakay, so let us derive the first equation. Oakay, so let us try to derive. I am showing the derivation of which equation? This is v is equal to u plus 80. Soo this is this equation gives a relation between. Soo this is a relation between velocity and time.

Vtelocity and time. Oakay, to derive this, let me consider a graph of uniformly accelerated motion. Oakay, so I am considering VtT graph, we know what do you mean by VtT graph, right?

Soo VtT graph of uniformly accelerated motion okay accelerated motion so we know you get a straight line say if this is v in y axis and this is t in x axis Soo in the previous case, we got uniformly accelerated when we got a straight line. Bdut straight line is always need not be from point 0. Oakay, so a straight line can be at any point. Let me take from this point, you know, you got a straight line. Oakay, so now this is your initial velocity.

The point where the object has started is initial velocity. If the object is started from 0, you would have got straight line from here. right so it is not always a zero initial velocity need not be zero always okay so it can be any value say the difference between the previous graph and this is just see i drew it from this point now i'm drawing it from certain point okay so the point where i started is my initial velocity that is u okay so let me consider this as a point a Oakay, so this is our initial velocity of an object.

Fine. And let this point be Bd, right? Oakay. Soo now what I will do is I will draw a line. Oakay, so this is the extended line.

Soo this is the line I draw perpendicular to y axis. I am calling it as let it be C. Oakay.

And a line that I draw perpendicular to x axis and let me call this as d right maybe these things are different in your ncrt textbooks right however you want you can name them however you want okay fine Soo now what I do is okay so one more line I will draw here okay so let me call this as point you know a is over b so let me call this as e okay fine and we all very well this is point o this is point o okay so what you can understand from a graph is this distance this much this o a let o a you OaA is initial velocity. This is initial velocity. This length, this, this length, this velocity on, you know, y axis, that is your initial velocity.

Oakay. Soo that is initial velocity. You always remember OaA is U.

Oakay. And let BdDc or, you know, C. Oakay. This C or BdDc, right?

Soo, this BdDc, if I take it on y-axis, this much is the length, okay? Soo, what is this final velocity? Oakay, so this is actually final velocity Vt.

Soo, BdDc, BdDc is final velocity, final velocity Vt, okay? And see here, OaDc. OaDc is time interval.

What is this gap? This is nothing but say if I consider this as t2, this is t1, t2 minus t1. That is time interval.

Soo OaDc is time. It is nothing but time t. Oakay, so now if I have to derive a first equation, let me consider the definition of acceleration.

Soo we studied what do you mean by acceleration? Acceleration is nothing but change in velocity, right? It is nothing but change in velocity by time. Right?

Soo what is change in velocity here? What is change in velocity? It is actually BdDc that is this much, this much, this is the final velocity minus initial velocity. Final velocity is how much?

Oakay, let me write it here. Change in velocity is nothing but final velocity minus initial velocity velocity right so what is final velocity final velocity is how much BdDc right so BdDc yeah divided by time Soo final velocity is BdDc. BdDc minus initial velocity.

Initial velocity is OaA. Oakay. Soee it is BdDc. BdDc means this much.

BdDc minus OaA. much this much is the change in velocity right so how do you get this much this minus this this minus this you will get this right so this is change in velocity this is what we calculated. Soo, how do you calculate this? This, what is this? BdDc, okay, minus TAOa or OaA, okay.

Soo, BdDc minus OaA divided by time is what? Time is what? Time is OaDc, right? Time is OaDc. Time is OaDc, right?

Soo, let me do it here. Soo, that's what. Soo, now acceleration, acceleration symbol is A.

Soo, acceleration is equal to BdDc minus OaA divided by OaDc. What is BdDc? BdDc is Vt I told. I took BdDc as Vt. minus what is o a o a is u divided by what is o d o d is t right so now this i will bring it with a i can write a t is equal to v minus u so this u if i bring it here you know how can i rearrange v is equal to v is equal to u plus a t i got my equation okay so this is the first kinematic equation first equation of motion Vt is equal to u plus 80 so hope you understood how we derived just you know I have drawn a straight line from a Oakay? And you know I have done a perpendicular line onto x-axis and a perpendicular line onto y-axis also.

Oakay? Soo what I just done is I have applied the formula of acceleration, the definition of acceleration. Acceleration is change in velocity by time.

Oakay? Soo change in velocity is how much? This is find. final velocity. Oakay?

Soo, this much minus this. Soo, this much is the change in velocity. How do you calculate this? This minus this right. Soo this we called it as v this o a we called it as u and this we know time interval.

Soo that that's what we substituted and got the formula right. Oakay so now we will go for deriving the second formula that is s is equal to ut plus half at square. Soee guys derivation of s is equal to ut plus half at square.

This is the relationship relationship between position and time okay so here s is actually distance from the same graph i can derive it easily yes is what i told s is nothing but distance right and do you remember in the previous i mean just a few minutes before we have learned how to find distance or displacement from vt graph it's nothing but the area covered right so here This area covered. Soo this is the area covered between A and Bd. Bdetween A and Bd, how much is the area covered? This is the area covered.

Oakay. Soo the area of Oa, A, Bd, Dc will give you the answer for distance. Oakay. What is yes here? Yes, that is nothing but distance.

Is area enclosed, area enclosed or area covered in OaADc. OaADc. Oakay, so this much is the area enclosed.

so what is this what is this o a b d is nothing but trapezium right so trapezium is again nothing but what trapezium is nothing but what it is it is this triangle plus this rectangle Oakay, so here OaADc is equal to what is that triangle A plus rectangle plus a rectangle o a e d okay o a e d okay so this is area of this area of o a b is nothing but area of triangle plus area of rectangle right okay so now area of oabd area of oabd is nothing but what yes right so s is equal to area of triangle area of triangle is what it is base into height what is base ye right into height. Height is BdE. Right?

Soo BdE. Oakay? A into BdE.

Oakay. And now plus area of rectangle is how much? Rectangle OaA DcE. Length into breadth.

Soo what is the breadth? OaA. OaA is the breadth of the rectangle. Oakay? Into?

Length. Length is how much? OaDc.

Right? Oakay. Soo, So is equal to A is what?

A. A is nothing but OaDc. Yes?

OaDc is nothing but time interval. Oakay? OaDc is nothing but time interval.

Right? Soo, A E is equal to OaDc. OaDc is equal to T.

Soo, I will write T here into BdE. Oakay. Let me discuss BdE.

Let me write it as BdE as of now plus OaA. What is OaA? OaA is initial velocity, right?

OaA is this much. This is nothing but initial velocity U. Oakay. Into OaDc. OaDcE is what?

Time interval, time interval, time gap. Soo that is T. Oakay, fine. Soo now we want the value of Bd.

Oakay, let me write that equation here. So is equal to T into BdE, right? Plus UT.

Soo we want to know what What is BdE here? Right? Oakay. Soo let's understand what do you mean by BdE? Soay actually speaking from VtT graph.

From VtT graph, we can calculate, we can calculate acceleration. What is that? We can calculate acceleration.

Oakay. Soo, you know, what do you mean by acceleration? How do we calculate acceleration?

Acceleration is nothing but change in velocity, right? Soo, it is nothing but change in velocity. by time.

Yes? Oakay. Soo, now what is change in velocity here that is from the graph?

Soee, this much. This much is, this is initial velocity, this is final velocity. This much is the change in velocity that is A. Oaur A is equal to BdE, no? A, see this length is equal to BdE, right?

Soo, here in case of change in velocity, I will write it as BdE, right? Soo, BdE and divided by time, okay? Time, let it be T. Soo, that means, can I write BdE is equal to A? Dcefinitely.

Soo, our BdE is equal to A. right? Soo, what I will write here So is equal to T E into Bd A is nothing but what?

A T, right? A T plus U T. Soo, what do I get? So is equal to A T square plus U T. That's what this I can also write it as So is equal to U T plus guys what we have forgot here area of triangle is actually half into half into base into height right so everywhere half we forgot so there comes half and here comes half right so here also comes half so what i can write here s is equal to ut plus half at square so somehow such mistakes are made right so everywhere we have to include that half Soo this is how we can derive So is equal to U T plus half A T square.

Right. Soo hope you understood the derivation. Anyway derivation is not that important. Remembering the equation is important.

Soo if you go for a higher level you will see that this equation is being derived from another means. Oakay. Soo by another concept. Soo as of now since it's mentioned in a textbook we are just deriving.

And now let me derive the third equation. Soay third equation I will derive it in a much simple way that is not from a graph. Just observe how do I derive a third equation. Soee guys observe carefully the derivation of this equation. Soee it's very simple if you go in this way right.

Soo we all know average velocity formula right. Average velocity formula we learnt in case of velocity. It is nothing but v plus u divided by 2. It's called average velocity.

Initial velocity, final velocity divided by 2 for uniform accelerated motion. Oakay. Soo now velocity v. is what?

The definition of velocity is what? We all know it is displacement. Vtelocity definition.

Instead of writing average velocity word, I am writing its definition. Dcisplacement divided by type, right, is equal to v plus u by 2. What is displacement? Dcisplacement symbol is yes, or distance or displacement is one and the same in this case.

Yes by t is equal to v plus u by 2. Soo, here s is equal to what I can write v plus u by 2 into t. Oakay, and I will shift this 2 here. Soo, I will write it as 2s is equal to v plus u into t. Oakay, so let me call this equation as 1. Oakay, fine.

And we know the equation, we know the first equation, what is that? v is equal to u plus at, right? I will shift this u this side.

Soo, v minus u is equal to at, I can write, right? Soo, here I can write a is equal to v minus u by t right. Soo the same equation I can write it in this way this is equation 2. Oakay, so multiplying equation 1 and 2, what do you get?

Multiply LHSo, Lhs. This is LHSo, this is Lhs. This is LHSo, this is Lhs. Multiply LHSo with LHSo. Soo, 2So into A.

Multiply Lhs with Lhs. How do you multiply? v plus u into t into this one.

v minus u by t. Soo, this t gets cancelled. Soo, what is remaining?

u v plus u. v minus u. Soo, what do you get?

v into v. v square and the v into u. Soo let me write it as minus VtU plus U into Vt, U, right? U plus U into minus U.

That will be minus U square. This minus U plus U gets cancelled. Soo what do you get guys? 2 A s is equal to v square minus u square, right? Soo, this is your equation, right?

Soo, very simple. Soo, this we know. Actually, from graph, this is what we will come to know.

From graph, okay so the distance how do you find it is the you know area of trapezium so when you take it from graph also this is the equation you will get and we know this equation on multiplying both of them we get the final equation this okay so it's very simple so we have discussed the derivation of all three equations and now we will see few important problems like how we can solve a problem if a question is asked okay Soo depending on all the equations we can solve a question. Soo let's see few numericals or problems that we have in our chapter. Look at the question number one guys.

A train starting from rest attains a velocity of 72 kilometer per hour in five minutes. Oakay so there is a train right and it was at rest it was at rest in the sense u is equal to 0 meter per second what is u initial velocity and it traveled for about 5 minutes and it is somewhere here right and this is the final position so the final velocity of a train is 72 kilometer per hour What they asked you to find out? Acceleration. Oakay, so u is equal to 0 meter per second.

Time is 5 minutes. Oakay, and this one velocity is 72 kilometer per hour. Convert this into meter per second. 72, right? Soo 1 kilometer is equal to 1000 meters, right?

Soo 72 kilometers is how many meters? It is 1000. Soee 72 kilometers. K, small k means 1000 divided by hour.

Soo 1 hour is equal to 3600 seconds. Soo 3600, okay? Soo if you do this calculation, how much do you get?

720 divided by 36. It is almost 20 meter per second. Soo this is your Vt. Oakay. Soo Vt is this much, U is this much. Time is 5 minutes.

Now convert it into seconds. Soo T is equal to 5 into 60. Soo 5, 6 are 30. Soo what? 300 seconds. Soo time must be in seconds, velocity must be in meter per seconds. Soo you have to first convert that if it is there in minutes and if it is there in kilometer per hour.

This is really very important. Soo now you calculate acceleration. Soo what is the formula?

Vt is equal to u plus a t. Right. Soo v minus u divided by t is equal to acceleration.

Right. Soo what is v? It is 20 minus u is 0 divided by time is 300. Right. Soo is equal to a. Soo what do you get?

20 divided by 300. This get cancelled. 1sr, 2 1sr, 2 5sr is equal to a. Soo a is equal to 1 by 15 meter per second square is the unit.

Soo this is the answer for first question. And coming to second question, what is the second question? Dcistance traveled by a train.

Whenever they asked about distance, right? You can use the formula So is equal to U T plus half A T square. Oakay.

Soo here U is 0 into time is 300 seconds. plus half into acceleration is how much just now you calculated it is 1 by 15 into times square that is 300 square right so s is equal to 0 into something 0 plus 1 by this 2 into 15 if you do how much do you get 2 5s are 10, 2 1s are 2, 3. Soo it is 30 into 300 square that is 300 into 300 you have to do. Right.

Soo 1 0 cancel with 1 0. Soo this is 1s are 1 0. right? 3 ones are 1, 0. Soo, 300 into 10, how much do you get? So is equal to 3000 meters or So is equal to 3 kilometer, okay? 1 kilometer is 1000 meters, no?

Soo, 3000 meters is 3 kilometers, okay? Soo, this is how you will solve the problem. Vtery simple, right?

Bdut converting is very, very important. There you have to be careful. Coming to second problem, very very important. Soee here, the brakes applied to a car produce acceleration 6 meter per second square in opposite direction of motion.

If car takes 2 seconds to stop, calculate distance it travels during this time. Soee there is a car, right? Oakay, and this car is moving and suddenly you applied brakes, okay?

Souddenly you applied brakes. And you know, soon after applying brake, it will not stop, right? It will move to a certain distance, right?

Soo, it moved to a certain distance and it stopped. Oakay. Soo, how much is the time took place for a car to move from here to here?

It is 2 seconds. That is the time. And what is the distance? This distance they are asking you to calculate.

Oakay. Soo, here. Acceleration you see acceleration is given 6 meter per second square but the acceleration in opposite direction if at all if they mention acceleration in opposite direction then a sign should be minus. A has a sign, Vt has a sign, U has a sign.

Oakay so here you have to be careful. Soay if something is there in opposite direction then sign have to be negative. Soo here a value should be minus 6 meter per second square. Oakay so now how do you calculate? They asked you to calculate distance right.

Dcistance when they asked you always use the formula s is equal to ut plus half at square. Soee here initial velocity is not given you have to calculate. Oakay see final velocity is how much? Soee after some distance car stops. Soo final velocity, velocity of a car when it is stopped.

Soo v is equal to 0. Oakay, a is equal to minus 6 meter per second square. Soo what is u guys? Soo calculate u now.

We know the formula v is equal to u plus 80. Right? Soo it is v minus 80 is equal to u. Soo your Vt is how much?

0 minus A is how much? Minus 6 into T is 2 seconds. Time is 2 seconds.

Oakay. Soo your U is equal to 12 meter per second. Isn't it? Soo that U value you substitute here. Soo U is 12 into time is 2 seconds plus half A is minus 6 into t square is 2 square.

Soo, here this will be 24, right, plus half into minus 6 into 4. Soo 2 1s are 2 2s are right. Soo 24 minus into plus minus 6 2s are 12. Soo So is equal to 12 meters is the answer. Soo that's all about the problem guys.

Soo here when you take a sign for acceleration you have to be very very careful. When they mention something if the acceleration is acted in opposite direction. then definitely a value must be minus okay so these are two examples and likewise the more examples you solve the more perfect you will become so apply the formulas just read the question properly try to understand if you can put one figure you feel it much easy what is given and what is that you have to calculate no your analyzation becomes easy when you put the figure Soo, use the formulas and calculate various numericals.

With this, I am completing this chapter. Motion. Oakay. Soo, hope you enjoyed the concept.

If you have understood, just post your opinion in the comments and meet you up with the next chapter. Soee you. Dco subscribe our channel to learn the concepts in the easiest way and in a detailed way.

Thank you.

Transcript for:Understanding Motion Through Graphs and Equations

Transcript for:
Understanding Motion Through Graphs and Equations