Speed and velocity

0:00- [Instructor] Suppose a car travels 100 meters in say, five seconds. The goal of this video is to figure out what is the speed of that car, how is it different than velocity, and how do we represent motion on a piece of paper? Let's find out. So let's start with speed.

0:21We define speed as the distance traveled by an object divided by the time taken to travel that distance. In our example, the distance traveled is 100 meters and the time taken to travel that distance, well it took five seconds to do that. So it's gonna be 100 meters divided by five seconds.

0:39What is 100 by 5? That is 20. And what is the unit of the speed? Well, let's see. It's meters divided by seconds. So we say the speed is 20 meters per second in this particular case. So just from this, we can now understand the meaning of the word speed. It tells us that the car is traveling 20 meters every second.

1:03That's how you think about speed. It tells you how much an object is traveling every second. Now, there are other units of speed. For example, in our everyday life, the unit of speed is miles per hour and it turns out 20 meters per second is roughly around 45 miles per hour.

1:21But don't worry about how we converted it. It's just to get a feeling for how big this number is. We'll stick to meters per second. And another caveat is that in this particular animation, the car was moving at a steady rate, but it's also possible that the car could have moved much faster in the beginning and then a little slower towards the end, still covering 100 meters in five seconds.

1:41In that particular case, the car literally does not travel 20 meters every second, but the speed value turns out to be the same because it's still covering 100 meters in five seconds. So in that particular case, what does this number mean? Well, in that particular case, this would be an average value.

1:57We say on average the car is driving 20 meters every second. And that's why this is actually called the average speed. Average speed is distance divide by time. But again, for our purposes, we don't have to worry about that, okay? We will only consider cases if the car is going at a steady rate in this video.

2:14So for our purposes, this literally means the car is traveling 20 meters every second, okay? Alright, so now comes the next question. How do we represent this on a piece of paper? Well, we do that by drawing a graph. So let's do that step by step, okay? So first, we draw a horizontal and we usually represent the time on the horizontal axis.

2:36Then, we draw the vertical, and we usually represent the distance on the vertical axis. So let's look at the distance traveled at different time intervals. Let's take one-second time interval. Here's what I mean. When time was zero, the distance traveled is zero meters.

2:50If I wait for one second, exactly one second, the car travels 20 meters. If I wait for two seconds, the car would've traveled a total of 40 meters. If I wait for three seconds, the car would've traveled a total of 60 meters, four seconds, the car would've traveled a total of 80 meters, and finally, after five seconds, the car would've traveled a total of 100 meters.

3:17Now what we can do is we can plot these values over here. So here is the distance values, and then here is the time values, and now let's plot them. The first plot is, the first point is at zero zero. So when the time is zero, the distance traveled is zero. So the first point is over here.

3:36So this particular point is located over here. Then, when the time is one second, the distance traveled is 20 meters. And so the way we can plot that is we can draw a line, a dotted line for 20 meters, a dotted line for one second, and we can say, "Hey, this point is over here, it's represented by this one," and we can keep doing that for two seconds, 40 meters.

3:57So here we go, for three seconds, 60 meters, four seconds, 80 meters, and finally, for five seconds we have 100 meters. And finally, we can connect all the dots and look, when you try to connect all the dots, what do we get? We get a straight line. This straight line represents this motion.

4:20This is how we can draw this motion on a piece of paper. Isn't that amazing? But wait, there's more. Remember the time that we calculated, five seconds? Here, it represents the horizontal. And the distance that we calculated over here, 100 meters? Here, it represents the vertical.

4:36And since speed is the distance divided by the time, in the graph, this represents the vertical divided by the horizontal. So we could say that in this distance time graph, if you take the vertical divided by the horizontal, you get the speed. And we could have calculated that vertical by horizontal wherever we want on the graph, and we would get the same result.

4:58For example, over here, look, we get 40 by 2, which is still 20 meters per second. So this quantity where we calculated the vertical divided by the horizontal, we give a name to it, we call it the slope. So slope is the vertical divided by the horizontal, or we can also call it the rise over the run, or in general, because the horizontal is usually labeled the X-axis and the vertical is labeled the Y-axis, we call this the change in the Y-coordinate and this represents the change in the X-coordinate.

5:31So we can also say it's the change in Y divided by the change in X, however you wanna think about it. I like to think about it as the vertical divided by the horizontal or the rise over the run. But why is it called the slope? Well, that's because it literally tells you how sloping or how steep the graph is.

5:46I mean, if the graph was steeper, look, the slope is much higher. You get a much higher vertical for the same horizontal. So I literally get a bigger slope. And because slope represents the speed, I can just look at this graph and say that, "Hey, this object is traveling faster than our car."

6:07That's amazing. Just by looking at this, I can tell, I can comment on the speed. Isn't that amazing? And similarly, what if the graph was less steep? Then look, for the same horizontal, I get a much smaller vertical, so I get a much smaller slope. And again, slope represents the speed and therefore, I can look at this and say, "Hey, this object is traveling much slower compared to our car."

6:29And what about this case? What if it's completely horizontal? Ooh, now the vertical just goes to zero. There is no vertical length anymore so the slope is zero. That means the speed is zero and that makes sense. Now, this object is not traveling any distance at all.

6:44It's always at zero. It's at rest. So isn't this beautiful? Just by looking at the slope, I can figure out the speed of the object. This finally brings us to velocity. What exactly is velocity? Well, velocity is just speed with direction. In our example, the car has a speed of 20 meters per second.

7:03But what is it's velocity? Well, it's velocity is 20 meters per second to the right because it's traveling to the right. Here's another example. Consider a bike that's going at 30 meters. It's traveling 30 meters every second. Well, its speed is 30 meters per second.

7:16But what is its velocity? Well, since it's traveling to the left, its velocity is 30 meters per second towards the left, and that's it. Okay, so putting it all together, we define speed as distance divided by time. It has a unit of meters per second. It's a measure of how fast something is moving.

7:32And we can draw a distance time graph, and the slope, which is basically the vertical divided by the horizontal, that represents the speed on this particular graph. And velocity is just speed with direction.