Displacement, velocity, and time
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Displacement from time and velocity example
Let's do one more example dealing with displacement, velocity, and time. So we have if Marcia travels for 1 minute at 5 meters per second to the south, how much will she be displaced? Let me do it this way. We know that velocity is equal to displacement divided by time. And it's really, once again, it is change in time. But we'll just say time. That's implicitly change in time. And if you manipulate this a little bit, you really just multiply both sides by time. You just multiply both sides by the variable t. You get displacement. Because this cancels out. You get displacement. And I'll flip this around. What's on the right-hand side, I'll write on the left. So you get displacement is equal to time times velocity or velocity times time. Is equal to velocity times time or velocity times change in time. So over here, they're asking us for displacement. They're asking us how much did Marcia get displaced? And they're saying that she travels for 1 minute. So this 1 minute right over here, this is her time. Sometimes you could view that as her change in time. Or it really is her change in time. If it said 0 minutes on her stopwatch when she started, at the end it'll say 1 minute. Or if it said 5 minutes, if maybe it was 3:05 when she started, it would be 3:06 when she finished. So it was really the change in time. Once again, I won't write the delta there just because this is the way you most frequently see it. But I want to tell you that these are the same thing for the purpose of this problem because sometimes you'll see the delta there. So the 1 minute, so the t right over here is 1 minute. At 5 meters per second to the south. This right over here is the velocity. They give us the magnitude, which is 5 meters per second. Or you could say that's the speed. And they also give us the direction, to the south. So this right over here is 5 meters per second to the south. So we might just say, look, if we want displacement, that's just going to be equal to 5 meters per second to the south times 1 minute. The problem here is that when we're talking about displacement, we're going to think about a magnitude of how much it's moved. So it'll be a distance of some kind. And some direction. We have our direction here, but we don't want any other units there. And if we just multiply this over here, we have 1 minute over here. But we have seconds in the denominator. You can't just cancel out a minute and a second. So you can't just say that you're going to get 5 and have some weird thing here. So in order for it to all work out, you have to either convert the 5 meters per second to 5 meters per minute. Or let me phrase that another way. You have to convert the 5 meters per second to some amount of meters per minute, not 5 meters per minute. It's going to be different. Or you convert the 1 minute to seconds. So at least in my mind, it's easier to convert 1 minute to seconds. So let's do that. So this is the same thing. 1 minute times. And we want to get rid of the minute. And the minute is essentially in the numerator right now. We could put this over 1. But it's essentially in the numerator. So we want to divide by minutes. And we want to multiply by seconds. We want seconds in the numerator. And so how many seconds are there per minute? You have 60 seconds for every 1 minute. And so you have a minute cancelling out with the minutes. And so now you have 5 meters per second to the south times 60 seconds. This is now cool because you have seconds and seconds. I wrote "sec" there, but this is also sec. So now you have seconds over seconds. Those cancel out. And so your displacement is going to be equal to 5 times 60. And then your units left are meters. All the time units have cancelled out and then it's meters to the south. So meters to the south. And this is equal to 5 times 60 is 300 meters to the south. And we are done. That's how much she has been displaced. If they just wanted the distance, you could say that she traveled 300 meters. Just that part. The magnitude of the displacement, that is the distance that she traveled.