Kinematics of motion in a straight line — practice question

A particle $P$ travels in a straight line from a point $O$ and is brought to rest $35\,\text{s}$ later. For $t\,\text{s}$ after leaving $O$, the velocity $v\,\text{m s}^{-1}$ of $P$ is given by $v = \frac{4}{5}t^2 \quad 0 \leq t \leq 5,$ $v = 2t + 10 \quad 5 \leq t \leq 15,$ $v = a + bt^2 \quad 15 \leq t \leq 35,$ where $a$ and $b$ are constants with $a > 0$ and $b < 0$.