Kinematics of motion in a straight line — practice question

A particle $P$ travels along a straight line, beginning from rest at a point $O$ on the line. After $t\text{ s}$ from leaving $O$, the acceleration of $P$ is $k(16 - t^2)\text{ m s}^{-2}$, where $k$ is a positive constant, and its displacement from $O$ is $s\text{ m}$. The velocity of $P$ is $8\text{ m s}^{-1}$ when $t = 4$.