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.