 So after a time t, it's going to be somewhere else. Now in order to figure out how it's going from one to the other, we need to know its acceleration and we also need to know its velocity. Just because it started on the left, and so it started with a negative position, doesn't mean it was going to the left. It could have had an initial velocity where it was heading to the right. So let's look at the initial velocity, so the initial velocity is a vector, it's got a direction, so it's either positive or negative if we're going one dimension. And we're going to call that u, so that's its initial velocity. And we're going to have to have a final velocity, and the final velocity can go in either direction, I'm just going to draw it to the right, assuming that it's going to be positive for the purposes of this diagram. And of course the reason we're working all of this out is that we've got an acceleration, so after a time t of acceleration, and again I'll direct that to the right, assuming the acceleration is in the positive x direction. Let's look at what happens graphically before we worry about the algebra, and so you have the acceleration doing nothing at all over time. So if I have time on one axis and acceleration on the other, we've already drawn on our diagram that it starts at a, a value of a, and it does not change, that's our idea, we're talking about constant acceleration, so it's like that. We've drawn it above the origin because our diagram has a positive number pointing to the right. Now what happens to velocity? Well we know that the velocity is changing at a constant rate, so it starts at u at time t equals zero, and then is going to increase because our acceleration is in the positive direction, it's going to increase up until it gets to our final value of v. And that should be a lovely straight line, I've drawn a reasonably straight line. Now what's going to happen to our position if that's going on? Well we start as a negative value on our diagram, so I'll have that there, so that will be our x naught, now if I'm going to write x naught on there, now I should write an x naught on here, always have things defined on your diagram, and if we're going to be moving and we end up at x final at a later time, now what's this shape going to look like? Well it's going to start off at some slope, and the slope here is going to be the slope given by our initial velocity, which is u. So if we break this up into a small amount of time, delta t, then we know that the velocity is the distance travelled over the time, and so the distance travelled is going to be the velocity times the time, or u times delta t. And up at the end it will work the same, except the velocity v is larger than you there, so the slope should be steeper. And somehow those slopes have to match, and so if we try and smoothly connect those curves, it's got to look something like that. Okay let's do the algebra for that, so we know that the acceleration is constant, and we know the definition of acceleration. So it's the change in velocity divided by the change in time. And so the change in velocity is going to be the final velocity minus the initial velocity, and the time taken we've written down as just t. If we multiply both sides by t, so if we multiply the left by t and the right by t, it's going to cancel that, and so we'll end up with at equals v minus u, and we can rearrange that. The most common way of arranging that one is as v equals u plus at, just adding u to both sides.