1. At time \(t\) seconds \(( t \geqslant 0 )\), a particle \(P\) has position vector \(\mathbf { r }\) metres with respect to a fixed origin \(O\), where

$$\mathbf { r } = \left( t ^ { 3 } - \frac { 9 } { 2 } t ^ { 2 } - 24 t \right) \mathbf { i } + \left( - t ^ { 3 } + 3 t ^ { 2 } + 12 t \right) \mathbf { j }$$ At time \(T\) seconds, \(P\) is moving in a direction parallel to the vector \(\mathbf { - i } - \mathbf { j }\)
Find

1. the value of \(T\),
2. the magnitude of the acceleration of \(P\) at the instant when \(t = T\).