2 A particle moves in a horizontal plane. The vectors \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors in the horizontal plane. At time \(t\) seconds, the velocity of the particle, \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\), is given by $$\mathbf { v } = 12 \cos \left( \frac { \pi } { 3 } t \right) \mathbf { i } - 9 t ^ { 2 } \mathbf { j }$$

1. Find an expression for the acceleration of the particle at time \(t\).
2. The particle, which has mass 4 kg , moves under the action of a single force, \(\mathbf { F }\) newtons.
   1. Find an expression for the force \(\mathbf { F }\) in terms of \(t\).
   2. Find the magnitude of \(\mathbf { F }\) when \(t = 3\).
3. When \(t = 3\), the particle is at the point with position vector \(( 4 \mathbf { i } - 2 \mathbf { j } ) \mathrm { m }\). Find the position vector, \(\mathbf { r }\) metres, of the particle at time \(t\).