Hey, guys. So you may come across some problems in which you have to calculate the velocity of one object that moves relative to or with respect to something else. So I want to introduce you in this video to the idea of relative motion or relative velocity. And really what we're going to see is that it kind of just comes down to simple addition and subtraction of velocities. So let's check it out. What's this whole idea about? Well, whenever we measure velocity, we are measuring it relative to some reference points, which we call a frame of reference. So for example, you're standing on the side of a road, you have a fancy speed gun or a radar gun that cops use to measure how fast you're driving and you're measuring the, you know, the speed of cars passing by. So your reference frame, your frame of reference is the earth. That's the thing that you're measuring those velocities with respect to. And so, in fact, most of the time in problems, your frame of reference is going to be the ground or the earth unless they otherwise tell you. So let's just jump right to an example so I can show you how this works. So imagine that you're an observer, right, and you're standing on the outside of a moving platform or a moving walkway like the kind that you see in airports. You have one of these fancy speed guns with you and you're going to measure the velocities of 3 different people on this moving walkway. So person a is standing still, person b is walking to the right, and person c is walking to the left. So what would our speed gun measure their velocities to be?

Well, the whole idea here is that if you look at \( t \) equals 0, all of these people are kind of lined up along the same position. But then one second later, the walkway has kind of moved everybody to the right. But because some of them are walking forwards, some of them are standing still and some of them are moving backwards, then they're going to be at different distances or different positions one second later. So what happens with person a? Well, what happens is the walkway is just going to move them some distance over, you know, some amount of time in one second. And so because person a is just standing still on the moving walkway that is moving them along at 3 meters per second, that if we pointed our speed gun at person a, it would also show them moving at 3 meters per second. So here's why. Here's a way you can visualize this. So imagine that my pen here is you, the observer. My hand is the moving walkway and person a is my red pen. So as the moving walkway basically moves this person along at 3 meters per second, they are together. And because they are together, they have the same velocity. In fact, whenever you have a stationary or not moving object that is inside or within or on top of another moving object, then they basically have the same velocity. They share the same velocity. And so in other words, another way we can say that is that the moving walkway and person a have the same relative velocity to all other reference frames. So to you, the observer, person a and the moving walkway have the same velocity relative to any other reference frame. And another way of also putting that is that they have the same velocity, then their velocities relative to each other are equal to 0.

So let's move on to person B now. So person B is moving along at 2 meters per second. So what happens with them? Well, in the same amount of time, the same one second, person B is because they're walking forwards, are going to travel a higher distance or greater distance in the same amount of time. Now we know that the velocity is equal to the change in position or the displacement over time. So if they're traveling a farther distance in the same amount of time, then that means that their velocity must be higher. So if we put our speed gun at B, what would we measure? Well, because B is moving at 2 meters per second, because they're walking forwards at 2 meters per second, then their 2 meters per second, in addition to the 3 meters per second, then the walkway is moving them along. Then when we point our speed gun at them, they're not going to be moving at 3, but they're going to be moving at 3 plus 2, which is 5 meters per second. And so what now happens with person c? Well, person c is moving 2 meters per second in the opposite direction. So in the same amount of time, they're going to cover a less distance than the other 2 persons a and b. And so their velocity must be lower than 5. So the idea is basically just the reverse. Their velocity relative to the moving walkway picks up a negative sign. And now what happens is if you were to point your speed gun at person c, it wouldn't measure 5, it wouldn't measure 3, it would measure 3 minus 2 because the velocity is pointed in opposite directions, so they kind of cancel each other out and you would see them moving at 1 meter per second. To summarize everything, really relative velocity is just the addition or subtraction of velocities, and it all depends on which directions those relative velocities are in. That's it for this one, guys. Let me know if you have any questions.