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Solving Constant and Average Velocity Problems

Patrick Ford
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Hey, guys. So oftentimes, in physics, you have to solve problems in which there is a constant or average velocity. So in this video, I'll show you how to solve these problems by using a slightly different form of the velocity equation which are already pretty familiar with. Let's check it out. Do you guys remember? The velocity is measured between two points an initial to a final position. So your textbooks might prefer this as an average velocity. Let's check it out. If you were going from 0 to 8, for example, in a span of four seconds, then your velocity is just Delta X, which is a change of eight over Delta T, which is a change in four. And so you get 2 m per second. But this velocity is often called an average velocity because you don't really know what happens in between. All you know is that you went from 0 to 8 and it took you four seconds. But during the middle, you could have sped up to 3 m per second, slowed down toe one and then sped back up again to three. You have no idea if you were to plot this out on a velocity versus time diagram that shows your velocity and y axis and your time in the X axis. It would look all squiggly like this because you're speeding up and slowing down. And this makes physics problems a nightmare to solve, because you have to sort of account for all the speeding up and slowing down. So one way we can sort of go around this is we can say, Well, we can kind of smooth out all of these velocities and pretend as if we were just traveling with a constant or average velocity that Smoothes out all of these different variations. So this is an average velocity. This makes things a lot easier in physics, because average velocities behave like a constant velocity in constant velocity. Problems in physics mean that there is no acceleration. And whenever there's no acceleration, there's only one equation that we're gonna use. And it's the one we already know. It's that V average or the velocity is just equal to Delta X over Delta T. That's it. That's the one equation that we're gonna use. Now we can take this equation and we can actually manipulate it to solve for Delta X because there's some problems. We have to be working with Delta X in the position. And so if we re arrange for this, we've got Delta X equals V average times Delta T All they did was just just move the delta t to the other side. And then some problems. There are some textbooks will start dropping this average over here. Now we can also do is take this Delta X and we know that this is just the X final minus X initial. So some textbooks and some equations will move this over to the other side. And what we get is we get this equation over here. X equals X not plus v times Delta t So again, this really is just a different form of this equation kind of just expanded out, and it gets a special name because it gets used a lot in physics. It's called the position equation. So later on, we're talking about the position equation. I'm talking about this guy over here, and it's called the position equation because it tells us that your final position X is just your initial position. X not plus how far you've moved that v times Delta T. And so we're gonna use this equation over here whenever we're solving for the velocity and we'll use this equation here. Whenever we're trying to solve the positions, that's all there is to it. Let's get some practice, guys. All right, so we're gonna solve for the unknown variables in each one of these diagrams here we've got from going from 0 to 20 and five seconds and we want to calculate velocity. So that means that we're just gonna go ahead and use the velocity equation here. So that means that our velocity is gonna be Delta X over Delta T. And so Delta X is 20 minus zero, right? That's my initial and final divided by a change in time of five seconds. So I just get 4 m per second. That's pretty straightforward. Let's move on. So now I've got my initial position, velocity and time, and I'm trying to find my final position. So now I'm gonna use my position equation just because it already gives me what the final position is gonna be is variable. So I've got X is gonna equal X not plus v times delta T So my final position is my initial position of two plus the velocity of three. And the change in time of six seconds. Three times six is 18 to plus 18 equals 20 m. So this is gonna be my final position right over here and for the last one. Let's check this out. Now we have to be a little bit careful, because if you notice in the first two diagrams who are moving to the right But in this last one here, we're actually moving to the left. So we have to be careful with that because we know this is gonna be the negative direction. This is gonna be the positive direction, and that makes sense because their velocity ends up being negative here. But we're still just looking for the initial position now. So we're gonna start off by using the position equation. X equals X not plus V times Delta T. So if I'm looking for this initial position, then I could just move all of this over to the other side. So I get X minus V times Delta T is equal to X. Not so. Let's just make sure I have everything I know what my final position is. I know what the velocity is. What about the change in time? Delta T? Well, I have my final and initial times. That's not Delta T. So I could just quickly go ahead and say, Well, these two Delta teas, they're gonna be t final minus t initial. So this is just gonna be seven minus three, which is four seconds. So now I have my delta t and now I can go ahead and plug everything in, so my final position is gonna be negative. 20. You plug it in with the signs and be careful minus my initial of my Sorry, My velocity is negative. Four again. Be careful with the signs. And then delta T is four seconds. And so these end up canceling out so you can You can make them both positive and you get negative. 20 plus 16 is equal to Delta are my initial position. And if you work this out, this ends up being negative 4 m. And that's our answer. That's our initial position. Alright, guys, that's it for this one. Let's 4 m. Let me know if you guys have any questions