Position, velocity, and speed | Physics | Khan Academy

Let's explore the ideas of position, speed, and velocity. So let's start with an example. We have a car parked here somewhere on the road. What is its position?

So let's start with that. What is its position? Well, the meaning of position is basically location. That's it; that's what position is. But how do I measure that? Well, for that, we need a reference point. You always measure the location by measuring how far it is from some reference. So, for example, let's choose this as our reference. We usually call the reference as over zero, or you can call that as an origin, whatever you want. It's not necessary, but it's convenient to that.

Now we can take some measurements. So if you measure this, let's say it turns out to be 10 m. We can now say, "Hey, the position of that car is 10 m." But you can immediately see one problem with this. If I just said the position is 10 m, we wouldn't know whether we're talking about 10 m to the right or 10 m to the left.

Therefore, one way to resolve this is to say the position is 10 m to the right. Okay, but another way to say the same thing is that we could choose all the markings on the right side of that origin to be positive and everything else on the left side to be negative. So now we could say the position of that car is +10 m. That automatically means it's 10 m to the right.

Now again, it's not necessary to choose the right side to be positive; we can choose the left side to be positive as well. You're completely free to decide that; it's just that it's more of a convention to choose the right side to be positive. Similarly, if the car was parked, say, on a vertical track, then we would usually choose upwards to be positive. Again, that's a convention, but we usually do that.

As a result of that, look, the position of this car became -15 m. The minus represents it's below our reference point.

Anyways, we can go ahead and write down the position. We usually use the letter x to denote the position, but again, you can choose whatever you want. It's more of a convention to do that. So in our case, x = 10 m. You could write plus 10 to represent that plus on the positive side, but even if you don't write plus, it's understood. So if you don't have any sign in front of it, it already means it's positive.

But I could have also written 10 m to the right. I could have drawn an arrow mark like this. All of them represent the same thing. But you can see what's important is that to represent position, you need both the magnitude (10 m) and the direction (as a sign or you use an arrow mark). So quantities that have both magnitude and direction are called vector quantities.

So position is a vector quantity because it requires a direction, and we represent that by using an arrow mark. What's important about the value of the position is if we had chosen a completely different reference point, let's say we had chosen our reference point to be somewhere over here. Let's say somewhere over here. Now look, the position of that car has changed even though the car has not moved. Its new position is -5 m.

That's because the reference point changed. So the value of this position value depends on where you choose your reference point. Another way of saying this is that the position depends on the reference frame. So it's always important to know where your reference point is and which you've chosen, positives and negatives.

Anyways, coming back, now let's make that car actually move. Let's say that car moves from here to here in 3 seconds. Now we can define a new quantity called velocity. Velocity is a measure of how quickly the position of the car changed.

We calculate it as change in position. This triangle means Delta; it means change in position divided by the time taken for that change in position. So in our example, in our example, what is the change in position?

Well, it was here to begin with; it went here. So from 10 to 25, the position has changed by 15 m. How do I get that 15? Well, I just did 25 minus 10, right? So I did 25 m minus 10 m; that's the change in position.

Divided by time taken, which is 3 seconds. So 25 - 10 is 15. 15 by 3 is 5 m per second.

So what does this number mean? Well, first of all, we see a positive sign over here. That means that velocity is to the right, and that makes sense. The position has changed to the right side. Velocity is also a vector quantity, okay? Because position is a vector quantity, so velocity becomes a vector quantity.

The sign tells you which direction the position has changed, that the new position is to the right side of my initial position. What does the number say? 5 m/s; it says that if the car was traveling at a constant rate, it would change its position 5 m to the right every second.

So if I could see an animation of it, this is what it would look like. In the first second, look, it changed by five; in the next second, it changed again by five to the right; in the last second, again it changed by 5 m to the right. Now, of course, you could ask, "What if the car was not moving at a constant rate? What if I was traveling a little faster earlier and then it became slower a little later?"

Well, then this no longer means it's traveling exactly 5 m/s. This would represent an average value, but let's not worry too much about it. Okay, let's take one more example. Let's say this time our car goes from here to here in 5 seconds. Why don't you figure out what the velocity is?

Alright, let's see. So velocity is... we need to figure out the change in position. How do we figure out the change in position? Well, it was initially here; it finally came over here.

So changing position is always final minus initial. That's exactly what we did earlier as well. So final position—oops, let's use the same color—final position, sorry, final position minus the initial position divided by the time taken for that change.

And so what will we get? Well, this is 5 - 25, which is -20. -20 by 5 is -4. So this time I would get -4 m/s.

Okay, what does this mean? Well, again, the minus sign is saying that the velocity, the position has changed to the left over here, and that makes sense. We see that we literally see the position has changed; the new position is to the left side of the initial position.

So that's what the negative sign says. But what does 4 m/s say? Ooh, it's now saying that if the car is going at a constant rate, the car would now be covering 4 m. It's changing its position 4 m to the left every second. It's a little slower than what we got earlier.

Now, speaking about faster and slower, that brings another quantity to mind, something that we're probably familiar with—that is speed. Well, think of speed as how quickly you travel some distance, and we calculate speed as distance over time.

Again, this would be true if the car was going at a constant speed. But if it was not, this would represent the average speed, just like before. But anyways, we can now ask, "What's the difference between speed and velocity?" They sound very similar, right?

Well, let's look at our examples one more time and calculate speed. Well, in the first case, what's the speed? Well, the speed over here was—or the average speed, I should say. What is the distance traveled? Well, the distance traveled is from 10 to 25; that is 15 m, divided by the time taken for that distance to be traveled, which is 3 seconds.

So 15 by 3 is five. I'm getting the same answer as before: 5 m/s. Again, what does this mean? This means that the car travels a distance of 5 m every second, as if it was going at a constant rate. But if it was not, then this would represent the average value just like before.

So in general, we usually call this the average speed. Okay, but this is the same as before. So what's the difference between speed and velocity? Ah, let's look at the second example; that will clear things for us. So if you go back to our second example where the car moved back, what is the speed now? Or what is the average—oops, okay, what is the average speed now?

Well, the average speed would be distance divided by time. Again, what is the distance traveled? This time, the distance traveled—the car came from here to here. So the distance traveled is 20 or is it -20? Well, when it comes to distance, I don't care about whether it's traveling to the left or it is traveling to the right; all I care about is the distance.

And the distance is 20, and that's the key difference. So over here, there will be no negative sign, so it'll be just 20 m divided by 5 seconds. So I get 20 by 5; that is just 4 m/s.

You can see there is no sign over here. This means the big difference between speed and velocity is that speed only has a magnitude; it does not have a direction because distance does not have a direction. I don't care about which direction it is moving, and since speed does not have a direction, it is a scalar quantity.

That's the big difference. You can think of speed as velocity without the direction. They both have the same units (m/s) as a standard unit, or in a more day-to-day life unit would be miles per hour.

So in short, the big difference between velocity and speed is that when it comes to velocity, we care about how much the position has changed. So, for example, if the car started from here and then, let's say, it came back to that same position, the changing position is zero because the car has come back to the same position, right?

So, as far as velocity is considered, there is no change in position. But when it comes to speed, speed says, "Well, I don't care about where your initial and final position is; all I care about is how much distance you travel." And you have traveled some distance, right?

Distance represents—you can think of it as the odometer reading in your car. That number will keep going up, right? So you would have traveled some distance, and so the distance traveled in this round trip would not be zero.

So you see, velocity is a vector quantity; direction matters. But when it comes to speed, the direction doesn't matter.