Kinematics of motion in a straight line — practice question

A particle $P$ travels along a straight line. It begins from rest at point $O$ and heads towards point A on the line. For the first $8\,\text{s}$, its speed rises to $8\,\text{m s}^{-1}$ with constant acceleration. Over the following $12\,\text{s}$, its speed falls to $2\,\text{m s}^{-1}$ with constant deceleration. $P$ then continues with constant acceleration for $6\,\text{s}$, arriving at A with speed $6.5\,\text{m s}^{-1}$. The displacement of $P$ from $O$, at time $t$ seconds after $P$ leaves $O$, is $s$ metres.