6. A man travels in a lift to the top of a tall office block. The lift starts from rest on the ground floor and moves vertically. It comes to rest again at the top floor, having moved a vertical distance of 27 m . The lift initially accelerates with a constant acceleration of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) until it reaches a speed of \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It then moves with a constant speed of \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for \(T\) seconds. Finally it decelerates with a constant deceleration for 2.5 s before coming to rest at the top floor.

1. Sketch a speed-time graph for the motion of the lift.
2. Hence, or otherwise, find the value of \(T\).
3. Sketch an acceleration-time graph for the motion of the lift. The mass of the man is 80 kg and the mass of the lift is 120 kg . The lift is pulled up by means of a vertical cable attached to the top of the lift. By modelling the cable as light and inextensible, find
4. the tension in the cable when the lift is accelerating,
   (3)
5. the magnitude of the force exerted by the lift on the man during the last 2.5 s of the motion.
   (3)