CIE May 2020 9709 Mechanics Paper 42 (pdf)
- A tram starts from rest and moves with uniform acceleration for 20 s. The tram then travels at a constant
speed, V m s−1, for 170 s before being brought to rest with a uniform deceleration of magnitude twice
that of the acceleration. The total distance travelled by the tram is 2.775 km.
(a) Sketch a velocity-time graph for the motion, stating the total time for which the tram is moving.
(b) Find V
(c) Find the magnitude of the acceleration.
- Coplanar forces of magnitudes 20 N, P N, 3P N and 4P N act at a point in the directions shown in the
diagram. The system is in equilibrium.
Find P and θ
- A particle of mass 2.5 kg is held in equilibrium on a rough plane inclined at 20° to the horizontal by a
force of magnitude T N making an angle of 60° with a line of greatest slope of the plane (see diagram).
The coefficient of friction between the particle and the plane is 0.3.
Find the greatest and least possible values of T.
- Small smooth spheres A and B, of equal radii and of masses 4 kg and 2 kg respectively, lie on a smooth
horizontal plane. Initially B is at rest and A is moving towards B with speed 10 m s−1. After the
spheres collide A continues to move in the same direction but with half the speed of B.
(a) Find the speed of B after the collision.
A third small smooth sphere C, of mass 1 kg and with the same radius as A and B, is at rest on the
plane. B now collides directly with C. After this collision B continues to move in the same direction
but with one third the speed of C.
(b) Show that there is another collision between A and B
(c) A and B coalesce during this collision.
Find the total loss of kinetic energy in the system due to the three collisions
- A car of mass 1250 kg is moving on a straight road.
(a) On a horizontal section of the road, the car has a constant speed of 32 m s−1
and there is a constant
force of 750 N resisting the motion.
(i) Calculate, in kW, the power developed by the engine of the car
(ii) Given that this power is suddenly decreased by 8 kW, find the instantaneous deceleration of
(b) On a section of the road inclined at sin−1 0.096 to the horizontal, the resistance to the motion of
the car is (1000 + 8v) N when the speed of the car is v m s−1. The car travels up this section of
the road at constant speed with the engine working at 60 kW.
Find this constant speed
- A particle P moves in a straight line. The velocity v m s−1
at time t s is given by
v = 2t + 1 for 0 ≤ t ≤ 5,
v = 36 − t2 for 5 ≤ t ≤ 7,
v = 2t − 27 for 7 ≤ t ≤ 13.5.
(a) Sketch the velocity-time graph for 0 ≤ t ≤ 13.5
(b) Find the acceleration at the instant when t = 6
(c) Find the total distance travelled by P in the interval 0 ≤ t ≤ 13.5.
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