1. 1. At time \(t\) seconds, where \(t \geqslant 0\), a particle \(P\) moves so that its acceleration a \(\mathrm { ms } ^ { - 2 }\) is given by

$$\mathbf { a } = ( 1 - 4 t ) \mathbf { i } + \left( 3 - t ^ { 2 } \right) \mathbf { j }$$ At the instant when \(t = 0\), the velocity of \(P\) is \(36 \mathbf { i } \mathrm {~m} \mathrm {~s} ^ { - 1 }\)

1. Find the velocity of \(P\) when \(t = 4\)
2. Find the value of \(t\) at the instant when \(P\) is moving in a direction perpendicular to i
   (ii) At time \(t\) seconds, where \(t \geqslant 0\), a particle \(Q\) moves so that its position vector \(\mathbf { r }\) metres, relative to a fixed origin \(O\), is given by $$\mathbf { r } = \left( t ^ { 2 } - t \right) \mathbf { i } + 3 t \mathbf { j }$$ Find the value of \(t\) at the instant when the speed of \(Q\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)