Position, velocity, and speed

0:00- [Instructor] 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. So what is its position? Well, the meaning of position is basically location.

0:16That'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 a reference. We usually call the reference as a zero, or you can call that as an origin, whatever you want.

0:34It's not necessary, but it's convenient to do that. And now we can measure this. So if you measure this, let's say it turns out to be 10 meters, we can now say, "Hey, the position of that car is 10 meters." But you can immediately see one problem with this. If I just said the position is 10 meters, we wouldn't know whether you were talking about 10 meters to the right or 10 meters to the left.

0:57And therefore, one way to resolve this is to say, "The position is 10 meters to the right," okay? But another way to say that, to say the same thing that the position is 10 meters to the right, another way to say this is 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.

1:18And so now, we could say the position of that car is plus 10 meters. That automatically means it's 10 meters to the right. Now, again, it's not necessary to choose a right side to be positive. You can choose left side to be positive as well. You're completely free to decide that.

1:34It's just that it's more of a convention to choose right side to be positive. And 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. And now as a result of that, look, the position of this car became minus 15 meter.

1:55The 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 equals 10 meters.

2:12You 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 meters to the right. I could have written 10 meters.

2:28I would've drawn 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 meters, and the direction as a sign or you write it or you use an arrow mark, but you have both magnitude and direction.

2:44So 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. And 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.

3:06Now look, the position of that car has changed. Even though the car has not moved, its new position is minus five meters. That's because the reference point changed. So the value, this position value depends on where you choose your reference point. Another way of saying this is saying that the position depends on reference frame.

3:25So it's always important to know where you're reference point is, which direction 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 three seconds. Now, we can define a new quantity called a velocity.

3:48Velocity is a measure of how quickly the position of the car changed. And we calculate it as change in position. The 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?

4:11Well, it was here to begin with. It went here. So from 10 to 25, the position has changed by 15 meters. How did I get that 15? Well, I just did 25 minus 10, right? So I did 25 meters minus 10 meters. That's the change in position. Divided by time taken, which is three seconds.

4:32So 25 minus 10 is 15, 15 by 3 is 5 meters 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?

4:52Because position is a vector quantity, so velocity becomes a vector quantity. So the sign tells you which direction the position has changed, that the new position is to the right side of my initial position. And what does the number say? Five meters per second.

5:06It says that if the car was traveling at a constant rate, it would change its position five meters to the right every second. So if I could see an animation of it, this is what it would look like. So in the first second, look, it changed by five. And the next second, it changed again by five to the right.

5:21And the last second, again, it changed by five meters to the right. Now, of course you could ask, what if the car was not moving at a constant rate? What if it was traveling a little faster earlier, and then it became slower a little later? Well, then, this no longer means it's traveling exactly five meters per second.

5:39Then 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 five seconds. Why don't you figure out what the velocity is? All right, let's see. So velocity is, we need to figure out the change in position.

5:59How 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 velocity. Oops, let's use the same color. Final position, sorry.

6:13Final position minus the initial position, divided by the time taken for that change. And so what will we get? Well, this is 5 minus 25 is minus 20. Minus 20 by 5 is minus 4. So this time, I would get minus 4 meters per second. Again, what does this mean? Well, again, the minus sign is saying that the velocity of the the position has changed to the left over here.

6:41And that makes sense. So 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 four meter per second say? Ooh, it's now saying that if the car is going at a constant rate, the car would now be covering four meters.

6:55It's changing its position four meters 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 in our mind something that we are probably familiar with. That is speed. Well, think of speed as how quickly you travel some distance.

7:15And we calculate speed as distance over time. And 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, "Well, what's the difference between speed and velocity?"

7:31They 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 travel is from 10 to 25.

7:48That is 15 meters divided by the time taken for that distance to be traveled, that is three seconds. And so 15 by 3 is 5. I'm getting the same answer as before, five meters per second. Again, what does this mean? This means now the car travels the distance of five meters every second, that if it was going at a constant rate.

8:07But if it was not, then this would represent the average value just like before. So in general, we just usually call this the average speed, okay? But this is the same as before. So what's the difference between the speed and velocity? Ah, let's look at the second example.

8:20That will clear things for us. So if you go back to our second example where the card 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 divide by time. Again, what is the distance traveled?

8:36This time, the distance traveled, a car came from here to here, so the distance traveled is 20. Or is it minus 20? Well, when it comes to distance, I don't care about whether it's traveling to the left or it's traveling to the right. All I care about is the distance, and the distance is 20.

8:51And that's the key difference. So over here, there will be no negative signs, so it'll be just 20 meters divided by 5 seconds. So I get 20 by 5. That is just 4 meters per second. And you can see there is no sign over here. This means the big difference between speed and velocity is speed only has a magnitude.

9:15It 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.

9:29They both have the same units, meters per second 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.

9:42So for example, if the car started from here, went over 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.

9:56But 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've traveled, and you have traveled some distance, right?" Distance represents, you can think of it as the odometer reading in your car.

10:09That 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.