 Now let's look at a problem solving strategy for constant acceleration situations. As a reminder, there's five equations we could use when we're solving constant acceleration problems. The first two of these were derived straight from the calculus, the third one was derived from the definition for the average velocity, and the other two are just algebraic rearrangements of these other ones that are just make it a little bit more convenient for us to work with. So we've got five variables in total that are represented in all of these equations, and again I want to remind you that some textbooks don't use the v initial with the v sub i, they might use v not for the velocity at time zero. Now the general outline for our problem solving solution is to create your list of the table of variables, fill in your knowns, use the rule of three, select the right equation, do your algebra, plug in your numbers, and then check your final answers. So when I say you list your variables near this table that we're dealing with, it's kind of something like this, where you've got delta x, v i, v f, a and t, and I just kind of keep them in a standard order, so I'm always looking at the same thing. If I'm working in two dimensions, you actually have two lines, one for the x and one for the y, but keep in mind that time is the same on both sides of that equation. Fill in your known values as you get them. So let's start with an example. A cart rolls along a flat horizontal surface with constant acceleration for 10 seconds. It starts from rest and rolls forward 20 meters. So the first thing we note here is this is a constant acceleration problem. If it's not constant acceleration, you can't even use this approach. So then we start with our blank table and we start to fill things in. So we'll notice, for instance, that we've got 10 seconds. Now it doesn't tell us that's the time, but if you're paying attention to your units, it's really obvious that 10 seconds has to be the time. The same thing with our 20 meters is going to be our displacement. And you might think those are the only knowns given in the problem because they're the only numbers listed, but remember, it starts from rest. That's going to imply that our initial velocity is 0 meters per second. So once you have three known values, then you can solve for either one of the unknowns. And when you're selecting the best equation, you want to pick out the one that has those three unknowns and the unknown you want. So going back to our example, that means we've got the displacement delta x, the initial velocity, vi, and the time. And so we can find either vf or a, either one of our two unknowns, because we've got three knowns. So let's say for now, for this example, that in addition to giving us the setup, it asked us to find the final velocity of the cart. So that means we need the equation with delta x, vi, vf, and t, but we don't need a. So when we go back and look at our overall equation summary, all of the equations have a in it except for this one right here, which has delta x, vi, vf, and t. So that's the one that we're going to want to select in order to have the conditions that we set forward in us problem. So bringing that over, we can then start to work with that to solve our problem. So the next step is your algebra. So we're solving for vf. We want to rearrange this equation using our algebra to find vf. And you probably want to double check this for yourself, but it ends up being two times the displacement divided by time minus the initial velocity. Once you've done that algebra, then you can actually plug in your values. I recommend that you do the algebra before you plug in the values, although some students will plug in their values and then do the algebra on that with the numbers in there. In this case, when we plug in our displacement, our time, and our initial velocity, we find that the final velocity is four meters per second. It's also a good idea to come back and check that. So once you've got that four meters per second, plug it back into that original equation. One half, the quantity is zero plus four meters, which would just be four meters. Half of that's two meters per second times our 10 seconds gives us 20 meters. So that works out both in terms of our numbers and our units. Once we've solved for that fourth quantity, we've got four quantities and only one unknown left. This times things get a lot easier. You can use any other equation now. Notice all of the other equations we have have the acceleration in them. I'm gonna suggest that this is the easiest one to use in this case. And if we take that equation, do our algebra to rearrange it, and then plug our numbers in, we find that our acceleration is 0.4 meters per second squared. You always want to come back and double check that, and you can either double check it with that equation you used to find it, or at this point you should be able to double check with any equation that no matter which things you plug in, you should be consistent with your table that's filled in now. So again, this is just one strategy that you can use to solve your constant acceleration equation problems.