1 A particle moves in a horizontal plane, in which the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed east and north respectively. At time \(t\) seconds, its position vector, \(\mathbf { r }\) metres, is given by $$\mathbf { r } = \left( 2 t ^ { 3 } - t ^ { 2 } + 6 \right) \mathbf { i } + \left( 8 - 4 t ^ { 3 } + t \right) \mathbf { j }$$

1. Find an expression for the velocity of the particle at time \(t\).
2. 1. Find the velocity of the particle when \(t = \frac { 1 } { 3 }\).
   2. State the direction in which the particle is travelling at this time.
3. Find the acceleration of the particle when \(t = 4\).
4. The mass of the particle is 6 kg . Find the magnitude of the resultant force on the particle when \(t = 4\).