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# Choosing kinematic equations

## Video transcript

in this video we're going to go through a few examples of setting up some problems with constant acceleration so we're not going to solve them we're just going to look at what we know and what the question is asking for and then identify which one of these equations over here will be the most useful for helping us solve it so Before we jump into the examples I want to say that it is very important to to understand where these equations come from to really develop a strong understanding of position and velocity and acceleration and time and how they're all related to one another and Sal has a lot of videos that go through that and and can help you build that understanding but once you have that understanding these equations are kind of like using a calculator where they help you save time it's important to to know how to add subtract multiply and divide so you know the calculator is doing when you use it but once you understand that the calculator is a really valuable tool and and that's what these equations are like they're tools that that we can use when we when we understand where they come from so with that out of the way let's let's dive into our example here so the question says a light rail commuter train accelerates at a rate of one point three five meters per second squared how long does it take to reach its top speed of 80 kilometers per hour starting from rest all right so let's let's unpack this and and see what it's saying so let's just start at the beginning a light rail commuter train accelerates at a rate of one point three five meters per second squared so that's pretty direct it's just telling us what the acceleration is so let's write that down the acceleration is one point three five meters per second squared all right there's one thing okay so let's keep going how long does it take to reach its top speed of 80 kilometers per hour starting from rest so that one's a little bit more complicated there's more going on in here but if we just start at the beginning and say how long does it take right that by itself is a question there's some more stuff afterward but that by itself is just asking about the time how long does it take all right so let's let's note that by by circling this time here we don't know what it is yet but this is our question whereas being asked about the time all right so if we keep going here we get all right how long does it take to reach the it's top speed of 80 kilometers per hour so that's saying its top speed is 80 kilometers per hour when it's done speeding up it'll it'll be going at 80 kilometers per hour so that's the final velocity or just our velocity at the time here so that's 80 km/h 80 point zero kilometers per hour and sometimes you'll see see this right here written as the sub F to really explicitly say it's the final velocity so the notation might vary in your physics class but so whatever notation you use that's fine but make sure to ask yourself what what is this symbol really talking about so anyway 80 km/h per hour okay and so we have that and then if we keep going it says starting from rest so that that's saying that at the beginning when it starts it's at rest which means it's at it has zero zero for its initial velocity it's just it's just sitting there so let's fill that in that's zero meters per second okay so we have analyzed this question and we see that actually the change in distance didn't appear anywhere in this question it's just just these four these four values right here so let's see if we can look at these equations and identify one that that has all of these things and and doesn't have Delta X since we don't know Delta X N and we're not looking for it either so we see these two have Delta X here and so so we can we can rule those out and this one also has two Delta X so we can rule that out so that leaves this one let's it has has velocity the final velocity here it has the initial velocity here has acceleration here and then it also has time which is what we're looking for so we can use this we've we've figured out that for this question right here we can just use that top equation alright and then and then to continue this we would plug in numbers and then and then solve for T and and see see what that time indeed is so for this video we're not going to actually go through that we're just going to go through another example of setting things up so let's go down to this question right here while entering a freeway a car accelerates from rest at a rate of 2.40 meters per second squared for 12.0 seconds how far does the car travel during those 12 seconds and what is the car's final velocity so this one actually asks two questions so let's just let's just focus on on the first one to begin with and l so let's see what we know so while entering a freeway a car accelerates from rest at a rate of 2.40 meters per second for 12 seconds so there's a lot of information here in this first sentence so let's let's see it says accelerates from rest right here accelerates from rest that tells us that the initial velocity is zero right from rest it wasn't it wasn't moving initially it was at rest so let's write that down this also just like the previous example had an initial velocity of zero meters per second that's not always the case but it happens that in these two examples it was so let's keep going so it accelerates from rest at a rate of two point four zero meters per second squared so that's that's telling us what the acceleration is two point four zero meters per second squared so let's write that down two point four zero meters per second squared meters per second squared and in all these problems it's important to think about whether something is moving in the positive direction or in the negative direction or if it's accelerating in the positive direction or the negative Drive it actually looks like for these examples we've chosen everything is is is moving in the positive direction and accelerating in that same direction so we won't have any negative signs pop up but it is important to think about that when you're doing these kinds of things just just in case something is negative and that does that does affect your answer and what's going on but anyway so so it's accelerating forward everything's going in the same direction so we're thinking of forward as the positive direction and they're accelerating that this this car is accelerating at 2.4 meters per second squared all right and it says also that it's doing that for twelve point zero seconds so we can write that down as well twelve point zero seconds all right so we know we know three things here and and you'll find that in problems like this that's the magic number once you have three of these you can you can find out the other pieces using these equations but anyway so the first question says how far does the car travel during those twelve point zero seconds well it's asking how far so that's going to be the Delta X here this change in position how far does it travel during those twelve seconds that's going to be this this value right here so this is our question circle it here so now notice we don't have this so we can look for an equation that doesn't have this this final velocity value in it and then that will be an equation that will hopefully have these other four but we'll have to check that so this one has that final velocity in it so we can rule that out I see this one also has the final velocity this one doesn't have the final velocity so let's look at that does it have so it has the position the change in position that's what we're looking for word has it right there the or sorry the initial velocity is right here so we have that as well let's see it has time in it and we have time so we will be able to plug that in and then finally it also has acceleration so it has everything we need it has the thing we're looking for and end it and it doesn't include anything that we that we just don't know that we're not even looking for so we found that for this problem right here this second equation here is going to be the one that is most useful for asking or answering the question how far does the car travel during those 12 seconds so that's that's for that question but this this block here actually has a second question maybe I'll switch to green let's let's look at this question what is the cars final velocity so all right so that means we're looking for this now right here what's this well we've already identified these these different pieces that we know and if we did the first part of the problem we would actually have a value 4 for Delta X here but assuming we didn't we didn't find that yet we could look at this and say what's the corresponding velocity I want to look for something that has V in it and and has these other three things that I know and if you look and you check through here let's see what is it so yeah I would actually end up being this one again this is that that equation that doesn't have the change in position in it and so just using the green color all I'll underline this here to say that this equation is useful for for this question and actually now that now that we have this value we could have used really any of them that had had RV in it so some options open up once we know more than three different things but anyway hopefully going through a couple of these examples that will be helpful for you and you run into your own questions and have to think there okay what do I have what am I looking for and then which equation will help me move forward in and solve this question