4 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 position vector, \(\mathbf { r }\) metres, of the particle is given by $$\mathbf { r } = \left( t ^ { 3 } - 3 t ^ { 2 } + 4 \right) \mathbf { i } + \left( 4 t + t ^ { 2 } \right) \mathbf { j }$$

1. Find an expression for the velocity of the particle at time \(t\).
2. The mass of the particle is 3 kg .
   1. Find an expression for \(\mathbf { F }\) at time \(t\).
   2. Find the magnitude of \(\mathbf { F }\) when \(t = 3\).
3. Find the value of \(t\) when \(\mathbf { F }\) acts due north.