We need to build backwards.
We know that the acceleration, which is the derivative of the velocity, is:
So, when we integrate with respect to time, we get:
We know that the initial velocity is when t = 0, and in this case is actually 0, so:
So, the initial velocity is a constant, which in this case is 0, making our velocity equation:
Now, we know that the velocity equation is the derivative of the position equation, , so we get:
We know that the initial position, we'll call this is the position at time t = 0:
So the initial position is constant, and in this case is also 0, so we now have our final position function (Plugging in ):
(Note: This is the equation you use for your runway problem)
The general equation is:
(Note: This is what you use when you have either a non-zero initial height/position or a non-zero initial velocity).