This sounds like a homework problem and not a science fair project which is what this site is intended to provide assistance with.
Have you had integral calculus? I'm guessing not or you probably should have quickly recognized that distance at some time d(t) = integral of velocity(t)dt over t=0,t
velocity v(t) = integral of acceleration a(t) = dV(t)/dt
a(t) is given as a constant function, so 78m/s divided by 20 s = 3.9 m/s/s (or meters per second squared)
And the rest would be a simple calculus problem.
For those without calculus, you need to look up equations or online calculators that are derived from the calculas solutions for specific cases. (Constant accelleration in your case).
If you put something like "Equation for distance under constant acceleration" into a search engine like "ask.com", one of the results is "Equations of Motion - Wikipedia" and if you click on the view article on Wikipedia, you get:
http://en.wikipedia.org/wiki/Equations_of_motion and if you click on "Equations of uniformly accellerated liner motion", there are the appropriate equations.
For the stated information, you can assume the initial distance si = 0 as the question asks for distance traveled. The initial velocity vi is given as 0 (rest).
So after dropping out all of the 0 terms, s = 0.5 * 78 m/s * 20 s.
If you have had algebra, you should be able to solve for the answer. If not, then it is time to learn algebra!