Calc. velocity from position time graphs

- [Instructor] My friend Mervyn and his wife had a race yesterday and I missed it. And I really wanted to see it, so I asked them, "Do you have a recording of it?" And they said, "Yes." So I said, "Good, give it to me." And they gave me this, a position-time graph of what happened. So let's look at this graph and see if we can figure out what happened at the race, who won the race, and who was faster? So a position-time graph gives us the position of any object at any instant of time. For example, this is Mervyn's graph, it says that at time zero, he was at zero. This is the starting line, let's say. At one second, he is over here, at one meter. At two seconds, he is at two meters and so on. And at the sixth second he is at six meters, at the finish line. So what we see from his graph is that it took him six seconds to finish the race. Now let's look at his wife. That's his wife, Nishal. Where was she at zero? Well, at time zero she's not in the picture at all. There is no graph of her. Ooh, that means she started late. That kind of makes sense, she's always late for things. At one second, again she's not there, nowhere to be seen. At two seconds, that's where she is at the starting line. Can you see that? She is at the starting line at two seconds. Okay. Let's see what happens at the third second. At three seconds she is already at three meters. Wow! She is fast! Do you see that? At two seconds she was at zero, at three seconds she's already at three meters. At four seconds she is already at six meters, she has finished the race. She wins at the fourth second. Mervyn takes six seconds to finish the race, she took only four seconds. In fact, really two seconds, because she came late, to finish the race. So clearly she won the race. And we can now kind of visualize what must have happened. And so clearly she was way faster than him. So let's see if we can now figure out what were their velocities. Let's start with Mervyn. So what was Mervyn's velocity for the entire race? Well, how do we calculate velocity? We calculate velocity as displacement over time. We have the time and we have the displacement. So can you pause for a while and see if you can figure out Mervyn's velocity yourself? Go ahead, pause, give it a try. All right, so Mervyn's velocity we'll call as VM. We will calculate over the entire six seconds. You can calculate over any time you want, but let's calculate over six seconds. So, over the six seconds his displacement was six meters. So his displacement was six meters, his time was, time taken for the displacement was six seconds, and so his velocity turns out to be one meter per second. So he travels at one meters every second. Now let's calculate Nishal's velocity. Again can you give it a try? Can you find out what Nishal's velocity is? Go ahead, give it a try. Okay, hopefully you have tried. Let's see. We'll do the same thing. Velocity for Nishal would be, again our displacement by time, so she starts over here and she ends the race over here. So we have to consider this time from two second to four second. So what was her displacement? Again, her displacement is from zero to six. So that's six meters. Her displacement is six meters. And how long it took her to do the displacement? It's not four seconds. She ends at four, but she started at two. So it took her two seconds to do that. Does that make sense? It took her two seconds to do that. And so that will equal six divide by two. That is three meters per second. So she was faster than Mervyn. Of course we had already figured that out, but her velocity is three meters per second. And now comes something super important to understand that is, if you look at Mervyn's graph one more time what you see is that every second he's traveling one meter first second, he travels one meter. Another second, he travels another meter. Next second again, he travels another meter. He is constantly traveling one meter every second. And that means his velocity is a constant. It's not changing. It's steady, it's a uniform motion. That's happening in the graph because the graph is a straight line. And the same is the case for Nishal as well. She is constantly traveling every second, three meters first second, three meters. Second second, three meters. Again, uniform motion because it's a straight line. So whenever position time graphs are straight lines it means the position is changing uniformly. Every second, same amount of change. Which means the velocity is a constant. On the other hand, if the graph was not a straight line if it was some kind of a curve like this, then we would see the the position won't change uniformly. And that means the velocity is not a constant. And of course, you've spoken a lot about this in previous videos. So if you need more clarity, great idea to go back watch those videos and then come back over here. Also, another important thing you can note is that Nishal who has a higher velocity her graph is steeper compared to Mervyn's graph who has a lower velocity. Can you see that? What I mean to say is if you treated this as mountains and if you were to climb these mountains Let's say you were climbing these mountains. Can you see to climb this graph it's a little harder because it's more steep. This is easier to climb because it's less steep. And so this means in a position time graph if something is steeper, that means it has a higher velocity. It kind of makes sense, right? More steep, that means quicker is the change in the position. And so at a glance, just by looking at which one is more steep we can figure out which one has more Velocity. All right, one last thing, it turns out there was another competitor in the race. There was a dog as well, and here is it's position time graph. So can you figure out what this dog did in this race? And find out what it's velocity was? I'm pretty sure you can. Please give it a try. All right, let's see at time zero, where is our dog? Well, it's over here. It starts directly at four meters. And then at one second, it is somewhere below. That means the dog is traveling in the opposite direction. At the end of five seconds notice it is back to the starting position. And so our dog is traveling in the opposite direction. That's what the graph is saying. So now let's go ahead and figure it out what it's velocity was. So we'll call that velocity as VD again, displacement over time. If we take five seconds as the time. Then initially the dog was over here. Finally at the end of five seconds, the dog is over here. So what's it's displacement? We might think it's four seconds, but it's not. We might think it's four meters, but it's not. Why not? Because notice it starts here and comes down. And so it's negative four meters. Another way to think about it, is that displacement is final position minus the initial position. So it's zero minus four which is minus four. And so anyways, you think about it. You see his displacement is negative four. It's traveling in the opposite direction. And how long it took him to do that? Well, it took it five seconds. So divide by five five seconds, that gives us negative four over five is 0.8. You can check that, it's negative minus 0.8 meters per second, pretty slow. And the negative sign is implying that our dog is going in the opposite direction. Even here if you think in terms of the mountain notice you are no longer climbing the mountain. As you go forward, you end up going downwards. Another way to see why it's the opposite of what we had before. Before you're climbing up, which we call as positive. Now you're going down, which we call as negative. However you wanna see it, the dog has a negative velocity because it's traveling the opposite direction. So what did we learn? We learned how to analyze position time graphs. We figured out how to calculate velocities from it. And we also saw if the graphs are straight line it means the position is changing uniformly. In other words, it's a uniform motion. Velocities are constants.