3.114: Displacement $s=(t+2)(4-2t)$; motion graphs

A particle $P$ moves in a straight line with displacement $s=(t+2)(4-2t)$ for $0\leqslant t\leqslant 5$. Find the values of $t$ for which the velocity is zero.

On the axes, sketch the displacement–time graph of $P$, stating the intercepts with the axes.

Sketch the velocity–time graph of $P$, stating the intercepts.

Find an expression for the acceleration of $P$ at time $t$.

Hence sketch the acceleration–time graph of $P$, stating the intercepts.