6 At time \(t\) seconds, where \(t \geqslant 0\), a particle P has position vector \(\mathbf { r }\) metres, where
\(\mathbf { r } = \left( 2 t ^ { 2 } - 12 t + 6 \right) \mathbf { i } + \left( t ^ { 3 } + 3 t ^ { 2 } - 8 t \right) \mathbf { j }\).
The velocity of P at time \(t\) seconds is \(\mathbf { v } \mathrm { ms } ^ { - 1 }\).
- Find \(\mathbf { v }\) in terms of \(t\).
- Determine the speed of P at the instant when it is moving parallel to the vector \(\mathbf { i } - 4 \mathbf { j }\).
- Determine the value of \(t\) when the magnitude of the acceleration of P is \(20.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).