The diagram shows the velocity-time graphs for the motion of two particles P and Q, which travel in the same direction along a straight line. P and Q both start at the same point X on the line, but Q starts to move T s later than P. Each particle moves with speed 2.5 m s^-1 for the first 20 s of its motion. The speed of each particle changes instantaneously to 4 m s^-1 after it has been moving for 20 s and the particle continues at this speed.

1. Make a rough copy of the diagram and shade the region whose area represents the displacement of P from X at the instant when Q starts. [1]
2. It is given that P has travelled 70 m at the instant when Q starts. Find the value of T. [2]
3. Find the distance between P and Q when Q's speed reaches 4 m s^-1. [2]
4. Sketch a single diagram showing the displacement-time graphs for both P and Q, with values shown on the t-axis at which the speed of either particle changes. [2]

A boy runs from a point A to a point C. He pauses at C and then walks back towards A until reaching the point B, where he stops. The diagram shows the graph of v against t, where v m s^-1 is the boy’s velocity at time t seconds after leaving A. The boy runs and walks in the same straight line throughout.

(i) Find the distances AC and AB.

(ii) Sketch the graph of x against t, where x metres is the boy’s displacement from A. Show clearly the values of t and x when the boy arrives at C, when he leaves C, and when he arrives at B.