1. In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

A fixed point $O$ lies on a straight line.

A particle $P$ moves along the straight line such that at time $t$ seconds, $t\geq0$, after passing through $O$, the velocity of $P$, $v$ ms^–1, is modelled as

$v=15–{t}^{2}–2t$

Verify that $P$ comes to instantaneous rest when $t=3$.