 Let's explore velocity time graphs. So velocity time graphs are basically a graph where you plot the velocity on the vertical axis and the time on the horizontal axis. So let's see what this graph is telling us. Imagine this is a graph of a car. So it says that at time t equal to zero, whenever we started our stop clock, the car's velocity was zero. Then notice there's a straight line. It climbs all the way to 16. That means for the next eight seconds, the velocity of this car is increasing. It keeps increasing all the way until it reaches 16 meters per second. Then what happens? Then look, there's a graph goes down. Does it mean the car is going back? No, no, no. This means now the velocity decreases. For the next two seconds, you can see the velocity decreases all the way to zero. That means over here at 10 seconds, the car comes to a stop. So can you imagine? The car speeds up, speeds up, speeds up, reaches a maximum speed. Then slows down, slows down, slows down, stops. And then what happens? And then you can see it becomes negative. What does negative velocity mean? Ooh, that means now the car will travel backwards and in reverse, in the opposite direction. That means now the car is speeding up. Again, look, the velocity is increasing in the negative direction all the way to 16. Again, minus 16. So it increases in reverse for the next two seconds. And then notice what happens. Then the velocity stays a constant. That means the car will keep moving but at a constant velocity. Now that's basically what the story is. And if you could visualize, this is what we would see. So let me just show you the animation of that. So here we have the car and here we have the timer and here we have kind of like the speedometer. So let's just look at it and see if it makes sense. We'll first see from zero to eight seconds. Boom, you see that? The car kept on increasing its speed. I have paused it, it did not stop. What happens next from eight to 10 seconds and from 10 seconds to next 12 seconds? The car will go from 16 to zero, zero to minus 16. So have a look at it. You see that? The car stopped and went in reverse. Now of course, speedometer does not have a negative sign. That's why it still shows 16 so its speed is still 16 but the velocity is negative 16 because it's traveling backwards now. And now we're over here and now what's gonna happen is it's gonna continue with the same velocity. Now the velocity will stay constant, uniform motion. Look at that. It will continue backwards at the same velocity. So that's basically how you make sense of velocity time graph. All right, so now let's see if we can solve a few questions on velocity time graph. Okay, so the first question we're gonna have is we want to calculate from this velocity time graph. What is the acceleration from zero to eight seconds of this car and what is the acceleration of this car from eight to 12 seconds? How do we do that? Well, let's see, I'm gonna try the first one and then probably you can attempt the second one. So we know the acceleration is calculated as final velocity minus initial velocity divided by the time taken. So for the first one, if you want to calculate from zero to eight seconds, your initial velocity would be the initial velocity here, which is zero. You can see it from the graph. Your final velocity will be over here, which is again, at eight seconds, will be here, which is 16 from the graph. So when you do v minus u divided by t, it'll be 16 minus zero divided by t and t is this number, eight. And so if we try to calculate it, it'll be 16 minus zero divided by eight and that give you 16 by two eight, which gives you two meters per second square. So see, you can calculate acceleration from the velocity time graph. Why don't you pause the video and see if you can calculate the second one yourself. All right, let's do this. We want to calculate acceleration from eight to 12 seconds. Again, we can use the same formula for acceleration. What is v over here? The final velocity. The final velocity is the velocity at this point, which is minus 16. And what is u over here? u is the velocity at initial velocity, but initial means eight at the beginning of this. This is initial. Eight, which is plus 16. And so if you plug in, your acceleration becomes minus 16, minus plus 16, this is the velocity here, divided by the time it took. So eight to 12 is four seconds, right? So four seconds to change the velocity. Notice we need to be careful with the negative signs over here, right? So it's minus 16, minus plus 16, that gives you minus 32 divided by four, giving you minus eight meters per second square. So this is telling that in the second case, the acceleration is negative. It's in the opposite direction. And that's the reason why eventually it's, you know, the car turned around. It's slowed down. So whenever things are slowing down, we say it's a deceleration or it's an acceleration in the opposite direction. That's basically what this means, okay. This time we're asked to calculate the displacement from the velocity time graph. How do we do that? Well, displacement is always the area under the velocity time graph. So if you want to calculate the displacement from zero to 10 seconds, we need to calculate the area under that part of the graph, which in this case becomes the area of the triangle. So the area of the triangle becomes half into base, which is this big, into height, which is this big. So if you do that, we get half into 10 seconds into 16 meters per second. And that gives me 160 divided by two, that is 80 meters. And just from the units, you can see why displacement is area under the VT graph. Because when you calculate the area, what are you doing? You are multiplying velocity with time. And when you do that, you can see the second cancels out and you end up with meters. So can you see why displacement also happens? Because when you're calculating the area, the units also tell you that it's a displacement. Okay, why don't you pause the video and try the second one yourself? What is the displacement from 10 to 15 seconds? All right, let's do it. So the displacement for the second one would be the area under this graph. And you can see either you can think of it as a trapezium or I like to think of it very simply as a triangle and a rectangle. So it'll be the area of this triangle, which is going to be half into base, which is two, into height. Need to be careful about the signs. Displacement can be negative as well. So if you have velocity to be negative, so this height is negative. So the minus 16 plus the area of the rectangle, which is just base into height. So again, the base is three this time and height is basically just this length, which is minus 16. So you get minus 64 meters. So this is telling that in the second case from 10 to 15 seconds, your displacement was negative. What does that mean? Well, the car traveled backwards, right? So that's what it's saying that the net displacement was negative. So this is how you can calculate acceleration and displacement from VT graph.