5. A particle \(P\) of mass 0.3 kg moves under the action of a single force \(\mathbf { F }\) newtons. At time \(t\) seconds \(( t \geqslant 0 ) , P\) has velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\), where
$$\mathbf { v } = \left( 3 t ^ { 2 } - 4 t \right) \mathbf { i } + \left( 3 t ^ { 2 } - 8 t + 4 \right) \mathbf { j }$$
- Find \(\mathbf { F }\) when \(t = 4\)
At the instants when \(P\) is at the points \(A\) and \(B\), particle \(P\) is moving parallel to the vector i.
- Find the distance \(A B\).