A cyclist starts from rest and moves in a straight line with acceleration \(0.5\text{ m s}^{-2}\) for \(10\text{ s}\). They then accelerate at \(1.5\text{ m s}^{-2}\) for a distance of \(13\text{ m}\), reaching a speed of \(v\text{ m s}^{-1}\). They then travel at speed \(v\text{ m s}^{-1}\) for \(5\text{ s}\). They then travel a distance of \(28\text{ m}\) whilst decelerating uniformly to rest.

(a) Find the value of \(v\).

(b)(i) Find the total distance travelled by the cyclist.

(b)(ii) Find the average speed of the cyclist for the whole of their motion.