The velocity-time graph models the motion of a car and consists of four straight line segments. From rest, the car accelerates at \(2\text{ m s}^{-2}\) to \(20\text{ m s}^{-1}\) over \(T\) seconds. It then decelerates at a constant rate for 5 seconds, travels at constant speed \(V\text{ m s}^{-1}\) for 27.5 seconds, and finally decelerates uniformly to rest in 5 seconds.

(a) Find \(T\). [1]

(b) The distance travelled before the car starts moving at constant speed is one third of the total distance. Find \(V\). [4]