Interpreting motion data

0:00- [Instructor] Let's learn about position-time graphs and position-timetables to analyze motion. Let's start by considering a car going at a constant velocity. To create a position-timetable, let's take snapshots of it at say every five seconds. So here we go, boom.

0:20And let's convert this to our familiar oil drop diagram. It's easier to work with dots. To mark positions, all we need is an axis, a vertical axis. Think of it as a number line and we need to start somewhere. So we need to call some point as zero. So let's just call this point as zero, and then we measure all the other points.

0:40Let's say when I measure this, it turns out to be 10 meters. If this distance is 10 meters, we will now say this position is 10 meters. You can imagine we have chosen upwards to be positive and that's why this is positive 10 meters. Then we'll measure how far this dot is from our origin.

1:00And let's say that happens to be 20 meters. In fact, that should be 20 meters because since we are going, since the car is traveling with a constant velocity, it travels the same distance, right? So if this was 10 meters, this would also be 10 meters. So the total would be 20 meters.

1:15And therefore this position now is 20 meters. Note that we are measuring always from the origin, not from here, from the origin. And same would be the case over here. This would be 30 meters, and this would be at 40 meters mark. Well, we now have our position and time recordings, so we can go ahead and fill up this position-time table.

1:38Why don't you give it a shot first? All right, let's do it. So at time zero seconds, our position was zero meters. Then at five seconds our position is 10 meters, then at 10 seconds, 20 meters. 15 seconds, it's 30 meters. And at 20 seconds we are at 40 meters.

2:00Ta da! This is how we draw our position-timetable. Now here's a question. If we were not shown the animation or we were not given this oil drop diagram could be just look at the position-timetable and comment on whether the car is accelerating or not. Sure. All we have to do is look at its displacement.

2:19So at zero we have the position zero. In the first five seconds it travels 10 meters. But look at what happens in the next five seconds. Again, it travels from 10 to 20, 10 meters. In the next five seconds, again it travels 10 meters. So can you see in every five seconds, it keeps traveling 10 meters.

2:40That's constant velocity. So just by looking at the position-time graph, you get the same information as we get from the oil drop diagram. So it's just another way of representing the same data. And guess what? There is another way to represent this data and that is by drawing what we call a position-time graph.

3:00Here we draw the time on the horizontal axis, and we draw the position on the vertical axis. And by the way, we tend to use the symbol X to represent the position. That's just a tradition for us. Now again, before I plot it, can you try to plot the position-time graph yourself first and see what kind of graph you end up with?

3:20All right, let's do this. Now ideally you need a graph paper to have very accurate markings, but since I don't have it, I'm gonna draw a few reference lines for myself. Cool. Now at zero time, our position is zero, so that's zero, zero, that's over here. At five seconds, our position is at 10 meters.

3:38So we draw here. 10 seconds, we are at 20. 15 seconds, we are at 30, and at 20 seconds, we are at 40. Can you see that all these points lie on a straight line? So this means that when things are going at a constant velocity, their position-time graph would be a straight line.

4:05And again, that's happening because at every five seconds your graph is incrementing by the same amount, 10 meters. Another five seconds, 10 meters, another five seconds, 10 meters. And that gives you a straight line. Finally, before we move on, what do you think is the velocity of this car?

4:21Feel free to use any of these because all the three are telling you the same story. All right, so how do we calculate velocity? Well, velocity is displacement over time. And for that, let's see if I can use the position-timetable to do that. Well, for this I just need to pick some time interval, and we are free to choose any time interval we want.

4:42So let's pick say from 10 to 15 seconds. So from 10 to 15 seconds, the time interval is five seconds. And in that time interval, what is the displacement? Well, you go from 20 to 30, that is 10 meters. And therefore what is your velocity? Your velocity is two meters per second.

5:03And could we get the same thing from our oil drop diagram? Sure, if you go from 10 to 15 in five seconds, it's covering 10 meters. The exact same thing. Do we get that, can we get that from the graph as well? Well let's see. If we go from 10 to 15, that five seconds is actually this length 'cause remember in the graph the horizontal represents the time.

5:30So this is the five seconds. And when we calculate displacement from 20 to 30, we are measuring this length because the vertical represents the position over here. And so what you notice is velocity over here is going to be the vertical divided by the horizontal.

5:49And that quantity, the vertical divided by the horizontal represents the slope. It literally tells you steep the graph is. So this means the velocity, or at least the magnitude of the velocity is given by the slope of the graph. And this is amazing because that means if I had another graph, let's say that looked like this.

6:12I can immediately say this is also an object going at a constant velocity because it's a straight line. But I can now compare it with this one and I can say, hey, this has less slope, and therefore it must be having smaller velocity compared to this. And you can confirm this for example, in five seconds our car is over here, but this object, this object is only here.

6:33So clearly it's going slower, but just by looking at the slope you can identify it. And similarly, if I had another object which had a graph like this, and imagine that's a straight line, then again you can say, hey, this is also an object moving at a constant velocity, but it has a much higher slope.

6:48Look at it how steep it is. Therefore it must be having a higher velocity compared to this. So that's amazing. That's why I love position-time graphs because just by looking at the slope, I can compare velocities. That is awesome. Can we check our understanding by taking a couple of more examples?

7:07Okay, here's the next one. This time I'm gonna give you a table, and why don't you pause and think about what this object is doing. Is it going with a constant velocity? Is it accelerating or decelerating? Why don't you pause and think about it. All right, just like before, I will look at the displacement.

7:23In the first five seconds, it covers one meter. In the next five seconds oh look, it covers, it goes from one to four, that means it covers three meters. In the next five seconds, oof look, it covers five meters. It's covering more and more distance. That means this car must be speeding up.

7:42Immediately I know that this object is accelerating, and if we can go ahead and draw the oil drop diagram for this, it will look something like this. I plotted the same story over here. And you see the same thing visually. It's covering more and more distance in every five seconds.

8:03And again, I encourage you to pause the video and see if you can plot the graph yourself first. All right, because I don't have a graph paper, I have drawn some reference lines. So again, for zero, we are at zero. At five, we are at one now. At 10 we are at four.

8:21So somewhere over here. At 15, we are at nine, that's over here. And at 20 we are at 16. Is this a straight line? Clearly no. That's not a straight line. Let's just just see that. There is no way this can be a straight line. I cannot draw a straight line. Instead it becomes a curve.

8:42And so when objects are accelerating, we get a curve. But now let's think about the slope. Clearly, because it's a curve, the slope is changing. But if you see here, the slope is less. It's, the graph is not very steep over here. But as I go forward, look, it becomes steeper and steeper.

9:00Imagine it's a mountain that you're climbing, it's easier to climb here, but it gets harder and harder to climb. So that means the slope is increasing. Ah, that means the velocity is increasing. So you see, again, the graph also gives you the same information that we got from here.

9:17Velocity is increasing. It is accelerating. Here's the final one. This time I'm directly giving you the graph. Can you analyze the motion? What is the object doing? Well, because it's a curve. I know that it's not constant velocity. Velocity is changing. But is it accelerating, decelerating?

9:33What is it doing? Well, let's look at the slope. Initially the graph is very steep. It's very hard to climb this, so very high velocity. But then notice as I keep climbing there, it becomes easier to climb. It becomes less steep. Ooh, the slope decreases. This means the velocity becomes smaller.

9:52So that means this object must be decelerating. And looking at the table and the oil dot diagram, they too tell the same story. And I'm sure you can confirm this yourself now.