2. A particle \(P\) of mass 1.5 kg moves under the action of a single force \(\mathbf { F }\) newtons.
At time \(t\) seconds, \(t \geqslant 0 , P\) has velocity \(\mathbf { v } \mathrm { ms } ^ { - 1 }\), where
$$\mathbf { v } = \left( 5 t ^ { 2 } - t ^ { 3 } \right) \mathbf { i } + \left( 2 t ^ { 3 } - 8 t \right) \mathbf { j }$$
- Find \(\mathbf { F }\) when \(t = 2\)
At time \(t = 0 , P\) is at the origin \(O\).
- Find the position vector of \(P\) relative to \(O\) at the instant when \(P\) is moving in the direction of the vector \(\mathbf { j }\)