AS APPLIED Unit 9 Kinematics 2 (variable acceleration)

A sled is moving down a steep hill in a straight line. At the time t s, the acceleration of the sled is a m s^-2 where a=1/500(20t^2-t^3), t is larger than or equal to 0, and smaller or equal than to 20. When t=0 the sled is at rest at the top of the hill. Find the distance the sled travels in the first 10s of its motion.
What i did was find a = 2 and go the answer 100m is that correct?

No, the acceleration is not constant (2). You integrate acceleration expression once to get v(t) then again to get s(t). In each case you have an initial conditiion so v(0)=0 and s(0)=0.