 We're now in a position to be able to look at constant acceleration in one dimension and the equations that we're going to be using for that situation. We're focusing just on one dimension for now. And by constant acceleration, we're referring to the fact that the velocity is changing at a constant rate, and you have one value for the acceleration at all times. It could be a positive value or it could be a negative value, but once you set it, that's the value for the entire problem. Remember that if there's no acceleration at any time during the problem, that's a special case of constant acceleration as well. Now our first equation for the position comes from calculus, and you may see it in several forms. One of those is the position as a function of time, where x naught and v naught are the position in the velocity at a time of zero. Now, some textbooks use an alternate notation where we're talking about the final position, the initial position and the initial velocity. If you take this form of the equation and just move the initial position over to the other side of the equation, that's our change in position or displacement. And just to emphasize that we're dealing with one dimension, some textbooks will go ahead at this point and specify that this is the x part of the velocity and the x part of the acceleration. Focusing in just right now on this form of the equation, what we can see is it involves four variables, the displacement, the initial velocity, the acceleration and the time. But one thing that's not in this equation is the final velocity. We'll see how that matters here in a minute. Then we get to our velocity equation, what I'm going to call equation number two. And again, it comes from calculus and you may see it in several different forms. From calculus, we get the velocity as a function of time, and it depends on the velocity at time zero. If we go ahead and change this into the notation common in our textbook, then we've got our final velocity and our initial velocity. You could rearrange this to look at the change in velocity being related to the acceleration in time. And again, you could emphasize that these are the x parts if since we're dealing with only one dimension. Taking a look at our sort of standard one we're going to be using, again, we see that there are four variables, the initial velocity, the final velocity, the acceleration and the time. And in this case, it doesn't have the displacement in there. So we have some of the same variables but also some different ones. Equation number three can also be used to write out the position, but this comes not from calculus but from the average velocity equation. If I have the average velocity defined as the displacement over a time period, and I take a look at the graph if I've got constant acceleration, that means my velocity graph is a nice straight line, and the average velocity is really easy to find because it's just the average between the initial and the final values. Rearranging the algebra on these equations, I get this new form of the equation. And so I've got my displacement, my initial and final velocities in my time, but not acceleration. So once again, it involves four variables but not one of our standard ones. Now equation number four is sort of an algebraic rearrangement. If I start with equations one and two that I've already been working with, and I look for some way that I could have the displacement, the initial final velocities in the acceleration, but not time, so I have to eliminate time between these equations using algebra, then I end up getting this form of the equation. It involves the final velocity squared minus the initial velocity squared, and that's equal to two times the acceleration times the displacement. My fifth equation again involves algebra with my equations one and two, but in this case I'm looking for a way to eliminate the initial velocity. This way I've got a whole set of equations, each which involve four variables but not one of them. And doing that algebra, I get an equation very similar to my first one, but I've got the final velocity and I've got a negative sign in there. Now to summarize these, I've got two equations that came to us from calculus. One equation that came to us from the definition of the average velocity and how that works if I've got constant acceleration. And then I've got two additional equations that show up when I do algebraic rearrangements of these. Now when you're actually solving problems, you want to choose the equation to use based on what you know and what you're looking for. The four things, you should have three that you know, one that you're looking for, and that will help you figure out which one of these equations to use.