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, \(t \geqslant 0\), after passing through \(O\), the velocity of \(P , v \mathrm {~ms} ^ { - 1 }\), is modelled as $$v = 15 - t ^ { 2 } - 2 t$$

1. Verify that \(P\) comes to instantaneous rest when \(t = 3\)
2. Find the magnitude of the acceleration of \(P\) when \(t = 3\)
3. Find the total distance travelled by \(P\) in the interval \(0 \leqslant t \leqslant 4\)