kinematics differentiation (distance travelled by particle)

and so i got thrown into the sea without knowing how to swim again... (Speechless)

A particle moves in a straight line so that at time t seconds after leaving a fixed point of origin O, it's displacement is s metres and is governed by the equation $\displaystyle s = 8\cos(\dfrac{\pi}{3}t + \dfrac{\pi}{6})$. The initial velocity(v) of the particle is $\displaystyle -\dfrac{4(\pi)}{3} m/s $. Find the total distance travelled when the particle comes to rest at t = 2.5s

I kind of got near $\displaystyle 8 + 4\sqrt3$ which is the answer when i differentiated s twice to get the acceleration so i figured the answer is derived from there but i can't seem to get to the answer.. any pointers? thanks!