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This page covers Questions and Worked Solutions for CIE Mechanics Paper 42 May/June 2020, 9709/42.

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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 the car.

(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 − t^{2}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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