Where d is distance traveled in a straight line, t is the number of seconds spent traveling, and a is the rate of acceleration, what is the equation for finding out how much distance you can travel?

 

For example, according to this article, the maximum time you can spend falling without taking damage with this spell is 18 seconds. So, where t = 18, and a = 9.8 (which is standard freefall acceleration), what's the equation for computing the maximum height you can fall from in this game?

I believe the answer is here: http://en.wikipedia.org/wiki/Acceleration#Uniform_acceleration

For an object undergoing constant acceleration, d = v₀t + 1/2 at² where v₀ is the initial speed, presumably 0 for this example.

 

Thus d = 1/2 at²

 

Your speed after accelerating will be v = at if you start from rest.

Distance is time multiplied by average speed. Average speed for a uniformly accelerating object starting from rest is half its final velocity. Final velocity would be acceleration times the time.