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Race cars with constant speed around curve

When acceleration could involve a change in direction and not speed. Created by Sal Khan.

Video transcript

So we have some race cars racing, right here. And I have an interesting question to ask you. If we assume that these cars are making this turn right over here, that all of them are making this turn at a constant speed of 100 kilometers per hour, my interesting question for you is, are these cars accelerating while they make this turn? So is acceleration happening? And you might say, well, gee, look, my speed was constant, it's not changing. If I looked at the speedometer for the car here, if I looked at the speedometer over here, it won't budge, it just stays at 100 kilometers per hour. I don't have any change in speed over time. And so then you might say that you don't have any acceleration. But then you might be saying, well, why would Sal even make this video? And why would that question even be interesting? And your second suspicion would be true, because these cars actually are accelerating despite having a constant speed. And you can pause it and think about that for a second, if want to. But I wanted to point this out to you, because in an example like this, the difference between speed and velocity starts to matter, speed being a scalar quantity only having a magnitude. And velocity being a vector quantity, being speed with a direction, having a magnitude and a direction. And to think about-- let's take a top view of this thing, and then I think it'll become a little bit clearer the difference between speed and velocity and why these things are accelerating. So if I were to take a top view of this racetrack-- I'll do my best attempt to draw it-- so it might look something like this. This is the top view. I could even draw this red and white. So red, just to give you the idea. So this is the red, and there's some white in between. Obviously I'm not drawing as many dividers as there are in the actual picture, but it gives you an idea of what I'm actually drawing. And then there's some grass out here, there's some grass over here, and then there's some grass over here. And let's focus on this orange car and this red car right over here. And this is a top view, so this is its path right over here. And we're saying it has a constant speed of 100 kilometers per hour. So if you think about its velocity, the magnitude of it's velocity is constant, it's 100 kilometers per hour. But what is happening to the direction of the velocity? Remember, velocity is a vector quantity. It has magnitude and direction. So up here, when it's starting to enter the curve, it's going in this direction. And you tend to show vectors by arrows like this. And what you do is, the arrow's going in the direction of the velocity, in this case, and normally you would draw the length of the arrow shows what is the velocity. The magnitude of the velocity, I should say. So it's velocity's constant. So the length of this arrow will always be constant. But as we see, it's direction changes. When it's halfway through the turn, it's not going in that same direction. It is now going in a different direction, and when it comes to the bottom of the turn, it's going in a very different direction. And the direction keeps changing as long as it is turning. And I'm not going to go into the math here. We're going to wait for the math on this a little bit later. But remember, acceleration is a change in velocity over time. Acceleration is equal to a change in velocity over time, or we could say over a change in time. And although the velocity's magnitude is constant here, it's direction is changing. If there was no acceleration on it, it's magnitude and the direction of it's velocity would be constant, and the car would just keep going in that direction. So somehow, the car's direction is changing inward over and over and over again. And so this is just kind of a little bit of a trick question, something for you to think about, we're going to discuss the math in more detail in future videos. But what's happening here is the cars actually are accelerating. And they're actually accelerating inwards, and that's what's changing inwards. And when I say inwards, they're being accelerated towards the center of the curve, and that's what's allowing their direction to actually change.