4. A particle \(P\) moves in a straight horizontal line such that its acceleration at time \(t\) seconds is proportional to \(\left( 3 t ^ { 2 } - 5 \right)\).
Given that at time \(t = 0 , P\) is at rest at the origin \(O\) and that at time \(t = 3\), its velocity is \(3 \mathrm {~ms} ^ { - 1 }\),
- find, in \(\mathrm { m } \mathrm { s } ^ { - 2 }\), the acceleration of \(P\) in terms of \(t\),
- show that the displacement of the particle, \(s\) metres, from \(O\) at time \(t\) is given by
$$s = \frac { 1 } { 16 } t ^ { 2 } \left( t ^ { 2 } - 10 \right)$$
(4 marks)