A man is driving a car on a straight horizontal road. He sees a junction \(S\) ahead, at which he must stop. When the car is at the point \(P\), 300 m from \(S\), its speed is \(30 \text{ m s}^{-1}\). The car continues at this constant speed for 2 s after passing \(P\). The man then applies the brakes so that the car has constant deceleration and comes to rest at \(S\).
- Sketch, in the space below, a speed-time graph to illustrate the motion of the car in moving from \(P\) to \(S\). [2]
- Find the time taken by the car to travel from \(P\) to \(S\). [3]