 So that's the first equation we often remember when we're talking about constant acceleration that relates the final velocity to the initial velocity and how much you're accelerating. It's a little bit harder to figure out where we're going to be because our velocity keeps changing. So let's just look at a particular time in the middle where we've got say a velocity v1. At that time if we look at a very small amount of time the velocity won't change very much and so if we take a small amount of time delta t then we know that the distance it's going to change is going to be delta x is going to be v1 times delta t and v1 times delta t is basically just a little rectangle that big it's the area of that rectangle and what we have to do is we have to have the little change in distance we get from that piece and the little change in distance we get from that piece and so on and so on and that what turns out to be just the area under this curve that's how far we go and again you can do that formally by going to calculus but if you just believe me that that's the area and you can kind of see it it's just the sum of all those little rectangles then it's the area of this rectangle plus the area of this triangle the area of this rectangle well that height is u and this length is t so that's just u times t and this height is v minus u and that length is t so this is going to be half of the product of those so it's v minus u times t that's the size of that big rectangle there and because it's the triangle we're going to have half of that so we're going to have to add this area and that area together to get the distance that we travel so the distance we travel is the final position minus the initial position and we've just agreed that it's going to be this ut the area of the rectangle plus v minus ut 012 which is the area of the triangle