5 A particle moves on a horizontal plane in which the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed east and north respectively. At time \(t\) seconds, the particle's position vector, \(\mathbf { r }\) metres, is given by $$\mathbf { r } = 8 \left( \cos \frac { 1 } { 4 } t \right) \mathbf { i } - 8 \left( \sin \frac { 1 } { 4 } t \right) \mathbf { j }$$

1. Find an expression for the velocity of the particle at time \(t\).
2. Show that the speed of the particle is a constant.
3. Prove that the particle is moving in a circle.
4. Find the angular speed of the particle.
5. Find an expression for the acceleration of the particle at time \(t\).
6. State the magnitude of the acceleration of the particle.