12 In this question the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in the directions east and north respectively.
A particle \(P\) is moving on a smooth horizontal surface under the action of a single force \(\mathbf { F N }\). At time \(t\) seconds, where \(t \geqslant 0\), the velocity \(\mathbf { v } \mathrm { ms } ^ { - 1 }\) of \(P\), relative to a fixed origin \(O\), is given by \(\mathbf { v } = ( 1 - 2 t ) \mathbf { i } + \left( 2 t ^ { 2 } + t - 13 \right) \mathbf { j }\).

1. Show that \(P\) is never stationary.
2. Find, in terms of \(\mathbf { i }\) and \(\mathbf { j }\), the acceleration of \(P\) at time \(t\). The mass of \(P\) is 0.5 kg .
3. Determine the magnitude of \(\mathbf { F }\) when \(P\) is moving in the direction of the vector \(- 2 \mathbf { i } + \mathbf { j }\). Give your answer correct to \(\mathbf { 3 }\) significant figures. When \(t = 1 , P\) is at the point with position vector \(\frac { 1 } { 6 } \mathbf { j }\).
4. Determine the bearing of \(P\) from \(O\) at time \(t = 1.5\).