6. A particle \(P\) of mass 0.5 kg is moving under the action of a single force \(\mathbf { F }\) newtons. At time \(t\) seconds, \(\mathbf { F } = \left( 1.5 t ^ { 2 } - 3 \right) \mathbf { i } + 2 t \mathbf { j }\). When \(t = 2\), the velocity of \(P\) is \(( - 4 \mathbf { i } + 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).

1. Find the acceleration of \(P\) at time \(t\) seconds.
2. Show that, when \(t = 3\), the velocity of \(P\) is \(( 9 \mathbf { i } + 15 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). When \(t = 3\), the particle \(P\) receives an impulse \(\mathbf { Q }\) Ns. Immediately after the impulse the velocity of \(P\) is \(( - 3 \mathbf { i } + 20 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Find
3. the magnitude of \(\mathbf { Q }\),
4. the angle between \(\mathbf { Q }\) and \(\mathbf { i }\).