Kinematics of motion in a straight line — practice question

A particle $P$ travels along a straight line and passes through a point $O$. Its velocity $v\ \text{m s}^{-1}$ at time $t$ seconds after passing $O$ is given by $v = \frac{9}{4} + \frac{b}{(t + 1)^2} - ct^2,$ where $b$ and $c$ are positive constants. When $t = 5$, the velocity of $P$ is zero and the acceleration is $-\frac{13}{12}\ \text{m s}^{-2}$.