5. At time \(t\) seconds ( \(t \geqslant 0\) ), a particle \(P\) has velocity \(\mathbf { v m ~ s } ^ { - 1 }\), where
$$\mathbf { v } = \left( 3 t ^ { 2 } - 9 t + 6 \right) \mathbf { i } + \left( t ^ { 2 } + t - 6 \right) \mathbf { j }$$
- Find the acceleration of \(P\) when \(t = 3\)
When \(t = 0 , P\) is at the fixed point \(O\).
The particle comes to instantaneous rest at the point \(A\). - Find the distance \(O A\).