Kinematics of motion in a straight line — practice question

A particle $P$ moves along a straight line. $P$ begins from rest at $O$ and reaches $A$, where it comes to rest again, in $50$ seconds. The speed of $P$ at time $t$ seconds after leaving $O$ is $v\,\text{m s}^{-1}$, where $v$ is defined as follows: For $0 \leq t \leq 5$, $v = t - 0.1t^2$, for $5 \leq t \leq 45$, $v$ is constant, for $45 \leq t \leq 50$, $v = 9t - 0.1t^2 - 200$.