Acceleration with Multiple Parts

by Patrick Ford
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Hey, guys, For this video, we're gonna check out how we solve problems where an object is moving under constant acceleration in one or multiple parts. And what we're gonna find is that it's exactly like how we solve any motion problem in general. So let's check it out. Now, remember, in these problems, organization is our friend here, so the situation is gonna be different. You got a guy running and speeding up or slowing down. But when there's multiple parts, the first thing you want to do is just draw the diagram and then list of five variables like any motion problem. So you have parts A to B and then B to C, and then we also have the whole entire interval over here, and now we just have to draw. Now we have to list are five variables. So we've got Delta X initial velocity, final velocity acceleration in time, But because there's gonna be two sets of them, I'm gonna have to assign them variables. So I'm just gonna give them little A to be. Now, my initial velocity is actually gonna be the velocity right here. So I'm gonna call this V a final velocity is gonna be right here. So I'm gonna call this V B. And then you've got the acceleration in the time. Now we just do the exact same thing for the second set. So Delta X from B to C. Now, my initial velocity is VB. My final velocity is V c and then the acceleration and time. And now, finally, you also remember we have the two different parts. But we also have the whole the whole entire interval and the only two variables that matter. There are Delta X from A to C and then delta T from A to C. So it's the total distance in the total time. Usually those are the two ones that are given or there I asked for. So once we have this or sort of organizational structure for all of our problems and we have the list of variables now the rest of us just picking equations. So let's just work out this example together and see how this stuff works. So we're told that we're driving at a constant 30 m per second and then we see a road hazard and it takes 300.7 seconds for us to react and stop. But then we decelerate and then come to a stop. So that means that there are two different intervals going on here. So the first step is always to set up the problem by drawing the diagram and then listing your five variables. So let's go ahead and do that. So I've got this little diagram here. This is the part where I haven't yet slammed the brakes and it takes 0.7 seconds for me to react. So this is the reacting part. And then also over here I've got Once I've slammed the brakes, Now I'm coming to a stop. So this is the stopping part. So now we're just gonna go ahead and list the five variables Delta X from A to B once we've actually labeled them right. This is a B and C, and now I've got my V A V b acceleration and time. Okay, so I don't know the distance for this first part. All I know is that I'm driving in a constant 30 m per second, which is my initial velocity. So this is right here and because it is a constant 30 m per second, that's also gonna be my final velocity when I get to the end of this first interval, which means that the acceleration is equal to zero. So acceleration of A to B is zero the same exact velocity. And we also know that it takes 00.7 seconds first to react and stop. So those are our numbers there. Now, let's do the second, uh, the same thing for the second interval. I don't know the distance from B to C. I don't know the stopping distance. All I know is that the initial velocity here is gonna be 30 m per second because that's what it is over here. And then I know that I'm gonna come to a stop. So a stop means that the final velocity is gonna be zero. And I know that the acceleration in this point is gonna be 6 m per second. But it's decelerating, so it's gonna be negative six and then finally, the time. I don't know how long it takes for us to come to a stop. So these are all of our basically are variables here. So the second step is for each part, we just have to identify the known and now with the target variables. So what is part a asking us for? It's asking us for how far we're traveling before we're applying the brakes. So which one of these 10 variables is that gonna be? Well, before the brakes is actually in this first part over here, and it's asking us for a distance. So it's actually asking us for Delta X A to B. So that's that second step there so we know what we're looking for. Delta X from A to B. Now the third step is just to pick the right equation that does not have are ignored variable. But it's a little tricky. Here is a little weird here because we actually have four of the five variables, and more importantly, the acceleration is equal to zero. And so, if you go to our list of equations here, remember that we have two kinds of motion equations. When the acceleration is equal to zero, there's Onley just one. It's constant velocity, so we actually don't have to pick any equations here because there's really only just one to use. So that's V. Abe is Delta X from A to B over ta to be. And if we can actually re arrange for this and then sulfur Delta X So this is gonna be V A B times ta be. So this is just gonna be 30 times 300.7. And if you work this out, this is gonna be 21 m. So that's the answer. So it's just 21 m and that's the distance. So let's move on to part B now and go through the list of steps. We've already drawn the diagram, and now we just have to figure out what the target variable is. So now it's asking us in part B for the time it takes to stop after applying the brakes. So which one of the 10 variables that apply to Well, it's a time that's after we apply the brakes. So it's gonna be in the second interval, So that's actually gonna be the time. From B to C. This is gonna be the variable that we're looking for here. So that's the second step. The third step now is picking the, um, equation without the ignored variable. So if you take a look here, we have to use our, um equations because the acceleration is not equal to zero. But if you'll notice Also, we we have three out of the five variables and this is the variable that we're looking for. So that means that they ignored one is gonna be the Delta X from B to C. I have nothing no information about it. And so the equation that does not have Delta X is gonna be the first equation. So that's the equation I'm gonna use. So one this the final velocity, which is V C. Is equal to the initial velocity V B plus the acceleration times time. So if you go through our list of variables here, I know V. C is zero. I know VB and I have the acceleration. The only unknown here is time, so I've got zero equals 30 plus negative six times TBC If you go ahead and work this out really quickly Uh, the time from B to C that's equal to five seconds. All right, so that's our answer. So now we know that this is actually equal to five seconds. So now finally, let's move on to part C. So again, let go through a list of steps. What is the target variable in part C. It's actually asking us for the total distance traveled. So remember the total distance is going to be total distance for the entire interval from A to C. That's gonna be Delta X from A to C. And remember that Delta X from A to C is really just gonna be a B and B c added together. Right? Remember, if this is 10 and this is 20 then the whole thing is 30. That's just an example. So basically an equation where you can use is Delta X from A to C is equal to Delta X from a B plus Delta X B to C. Some of the words it's just 21 because already know this plus whatever b to C is and this is gonna be my final answer. So I'm just gonna go real quick and figure out what that Delta X from B to C is. That's all I have to do. So let's go over here and do that. Delta X from B to C is what? Well, so now this is my target variable. So now I just have to pick the equation that does not have the ignored variable. But now, if you've taken a look here, I already have four out of the five variables, so there is no longer and ignored variable. And whenever this happens, you can actually pick any of the equations that has Delta X in it, right? It's the Onley, other unknown that's left so you can pick any one of these equations here that has Delta X. The choice is really up to you and you'll get the same answer every single time. So what I'm gonna use is I'm gonna use equation number three so Delta X b c is gonna be the initial velocity V b times TBC plus one half a times t squared and I actually have everything right. I have four of the five variables, so I'm just gonna plug it in. So Delta X from B to C is gonna be 30 times five plus one half times negative six times five squared. And if you work this out in the calculator, what you're gonna get, you're gonna get 75 m. So we just plugged that right back into their for the total distance. And so we have 21 plus 75 and that's going to equal 96 m and that is our final answer. Alright, guys, let me know if you have any questions, let's get some more practice.