9709/41/M/J/25q3 – Mark scheme

The diagram shows the velocity-time graph of the motion of a cyclist. The graph consists of three straight line segments. The cyclist passes a point O with speed 3ms^-1 and then accelerates for 10s with constant acceleration 0.5ms^-2. He then travels at constant speed for 30s before decelerating, coming to rest at a point P, covering a distance of 80m whilst decelerating.

(a) Find the total time taken for the journey from O to P. [3 marks]

(b) Sketch a displacement-time graph for the cyclist’s journey from O to P, showing on your graph the distances travelled after 10s and 40s. [4 marks]

9709/42/M/J/25q4 – Mark Scheme

A car is travelling along a straight horizontal road. The car passes through a point A, on the road, travelling at a speed of 15ms^-1, and then accelerates uniformly at 0.4ms^-2 for 30 seconds. The car then moves at constant speed for 3T seconds, where T<30. The car then decelerates uniformly at 02.ms^-2 and after a further T seconds passes through a point B on the road.

(a) Sketch a velocity-time graph for the motion of the car between points A and B. [2 marks]

The distance from A to B is 2750m.

(b) Find the value of T. [6 marks]

The car continues its journey from B, decelerating uniformly at 0.5ms^-2 until it comes to rest at a point C on the road.

(c) Find the total distance from A to C. [3 marks]

9709/42/M/J/25q3 – Mark scheme

The diagram shows a velocity-time graph which models the motion of a particle. The graph consists of 3 straight line segments. The velocity of the particle at time t s after passing a fixed point O is v ms^-1. The particle leaves O with a velocity of 5ms^-1 and accelerates at 0.75ms^-2 for 20s. The particle then decelerates for the next 30s. At t = 40, the velocity of the particle is zero. After t = 40, the particle starts to travel back to O, coming to rest at O at time T s.

(a) Find the value of T. [5 marks]

(b) Find the acceleration of the particle from t = 50 to t = T. [2 marks]

9709/42/F/M/25q2 – Mark scheme

A cyclist is travelling along a straight horizontal road at a speed of 4ms^-1 when she passes a point O. She accelerates at a constant rate for a distance of 42m, reaching a speed of V ms^-1. She maintains the speed of V ms^-1 for 50m and then decelerates at 2ms^-2 before coming to rest. The distance travelled while decelerating is 16m.

(a) Find the value of V [2 marks]

(b) Find the total time for which she is in motion from the instant that she passes O. [3 marks]

9709/41/O/N/24q4 – Mark scheme

A bus travels between two stops, A and B. The bus starts from rest at A and accelerates at a constant rate of a ms^-2 until it reaches a speed of 16ms^-1. It then travels at this constant speed before decelerating at a constant rate of 0.75a ms^-2, coming to rest at B. The total time for the journey is 240s.

(a) Sketch the velocity-time graph for the bus’s journey from A to B. [1 marks]

(b) Find an expression, in terms of a, for the length of time that the bus is travelling with constant speed. [2 marks]

(c) Given that the distance from A to B is 3000m, find the value of a. [3 marks]