Non-constant Acceleration has me stumped.

[philll]

Homework Statement

An object in a frictionless environment accelerates at a rate which increases by 2 m/s2 every second. after 15 seconds, the object reaches is maximum acceleration, and remains constant for a further 30 seconds before all acceleration ceases and it therefore travels at a constant speed for an indefinite period of time. How far had the object traveled after 60 seconds?

u = 0
t = 60

Homework Equations

s = ut + ½ at²

The Attempt at a Solution

I don't even know where to start. I'd like to do it primarily on my own though, so if someone could point me in the right direction, it would be greatly appreciated.

 

[kamerling]

for non-constant acceleration you have

$$v(t) = v(0) + \int_{0}^{t} a(t) dt$$


and $$x(t) = x(0) + \int_{0}^{t} v(t) dt$$

which you should know how to do if you try this problem.