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 integrate:

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).