Well, we can simply use this one formula:

Meaning the acceleration is constant, in this case, it is

So, we simply take the antiderivative to find the velocity function:

Well, we know that this equals the velocity, but it's in and not , so we have to convert it.

Now we set the constant equal to the initial velocity, seeing as it fits the equation to find the final equation:

And we know it slows down to 0, so:

We can generalize a formula from this:

Now we take the antiderivative of the right side of that function:

This is the position function, and we can assume that since the initial velocity was the C value, that the initial position value would be the D value:

So, this function is a function of position, which is commonly called s(t):

Now we plug in what we know (Assuming we started at position = 0):

There is your final equation.