3 A particle moves in a horizontal plane under the action of a single force, \(\mathbf { F }\) newtons. The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed east and north respectively. At time \(t\) seconds, the velocity of the particle, \(\mathbf { v } \mathrm { ms } ^ { - 1 }\), is given by $$\mathbf { v } = 4 \mathrm { e } ^ { - 2 t } \mathbf { i } + \left( 6 t - 3 t ^ { 2 } \right) \mathbf { j }$$

1. Find an expression for the acceleration of the particle at time \(t\).
2. The mass of the particle is 5 kg .
   1. Find an expression for the force \(\mathbf { F }\) acting on the particle at time \(t\).
   2. Find the magnitude of \(\mathbf { F }\) when \(t = 0\).
3. Find the value of \(t\) when \(\mathbf { F }\) acts due west.
4. When \(t = 0\), the particle is at the point with position vector \(( 6 \mathbf { i } + 5 \mathbf { j } ) \mathrm { m }\). Find the position vector, \(\mathbf { r }\) metres, of the particle at time \(t\).