4. 2D Kinematics

Intro to Relative Velocity

# Intro to Relative Motion (Relative Velocity)

Patrick Ford

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Hey guys. So you may come across some problems which 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, the idea of relative motion or relative velocity And really, what we're gonna 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 used 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 the velocities with respect, Thio. And so, in fact, most of the time and problems, your frame of reference is gonna be the ground or the earth unless they otherwise tell you. So let's just jump right into 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. Are moving walkway like the kind that you've seen airports. You have one of these fancy speed guns with you, and you're gonna measure the velocity of three different people on this moving walkway. So person a standing still Person B's walking to the right. The person sees 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 zero, 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 rights. But because some of them are walking forward, some of them are standing still and some of them are moving backwards. Then they're gonna be a different distances or different positions one second later. So what happens with person? A. What happens is the walkway is just gonna 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 m per second. And if we pointed our speed gun at person A. It would also show them moving at 3 m per second. So here's why. Here's a way you can visualize this. So imagine 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 m 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 and 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 the person A has the same relative velocity to all other reference frames. So to you, the observer, the person A and the moving walkway have the same velocity relative to any other reference frame in another way of also putting that is that they have the same velocity in their velocities relative to each other. is equal to zero. So let's move on to person B now. So person B is moving along in 2 m per seconds. So what happens with them? Well, in the same amount of time, the same one second person be is because Because they're walking forwards. We're gonna travel higher distance or a 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 the velocity must be higher. So if we put it, our speed gonna be, what would we measure? Well, because B is moving at 2 m per second. Sorry, because they're walking forwards at 2 m per second. Then there, 2 m per second in addition to the 3 m per second on the walkway is moving them along. Then when we point our speed gun at them, they're not gonna be moving at three. But they're gonna be moving at three plus two, which is 5 m per second. And so what happened now happens with person, see? Well, person sees moving 2 m per second in the opposite direction. So in the same amount of time, they're going to cover a less distance than the other two persons A and B, and so their velocity must be lower than five and three. And 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, see, it wouldn't measure five. It wouldn't measure three. It would measure three minus two because the velocities point in opposite directions and they kind of cancel each other out, and you would see the moving at 1 m per second. So in, you know, it's a summarize. Everything really relative velocity is just the addition or subtraction of velocities. And it all depends on which directions that those relative velocities Aaron that's it for this one. Guys, let me know if you have any questions

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