5. At time \(t\) seconds, \(t \geqslant 0\), a particle \(P\) has velocity \(\mathbf { v } \mathrm { ms } ^ { - 1 }\), where
$$\mathbf { v } = \left( 5 t ^ { 2 } - 12 t + 15 \right) \mathbf { i } + \left( t ^ { 2 } + 8 t - 10 \right) \mathbf { j }$$
When \(t = 0 , P\) is at the origin \(O\).
At time \(T\) seconds, \(P\) is moving in the direction of \(( \mathbf { i } + \mathbf { j } )\).
- Find the value of \(T\).
When \(t = 3 , P\) is at the point \(A\).
- Find the magnitude of the acceleration of \(P\) as it passes through \(A\).
- Find the position vector of \(A\).