- A particle, \(P\), moves along a straight line such that at time \(t\) seconds, \(t \geqslant 0\), the velocity of \(P\), \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), is modelled as
$$v = 12 + 4 t - t ^ { 2 }$$
Find
- the magnitude of the acceleration of \(P\) when \(P\) is at instantaneous rest,
- the distance travelled by \(P\) in the interval \(0 \leqslant t \leqslant 3\)