An elevator starts from rest at the ground floor and moves vertically upward. It accelerates uniformly at 2m/s2 for 3s, then immediately decelerates uniformly at 2m/s2 until it comes to rest at an upper floor.
(i) Taking the upward direction as positive, sketch a velocity–time graph for the entire motion, clearly marking all important numerical values.
(ii) Using the graph or otherwise, calculate the maximum speed attained by the elevator.
(iii) Determine the total vertical displacement of the elevator during the entire journey and state its sign.