1. A particle of mass 0.3 kg is moving with velocity \(( 5 \mathbf { i } + 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse \(( - 3 \mathbf { i } + 3 \mathbf { j } ) \mathrm { N } \mathrm { s }\). Find the change in the kinetic energy of the particle due to the impulse.
   (6)
2. At time \(t\) seconds, \(t \geqslant 0\), a particle \(P\) has velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\), where

$$\mathbf { v } = \left( 27 - 3 t ^ { 2 } \right) \mathbf { i } + \left( 8 - t ^ { 3 } \right) \mathbf { j }$$ When \(t = 1\), the particle \(P\) is at the point with position vector \(\mathbf { r } \mathrm { m }\) relative to a fixed origin \(O\), where \(\mathbf { r } = - 5 \mathbf { i } + 2 \mathbf { j }\) Find

1. the magnitude of the acceleration of \(P\) at the instant when it is moving in the direction of the vector \(\mathbf { i }\),
2. the position vector of \(P\) at the instant when \(t = 3\)