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### MATHEMATICS 9709

#### Cambridge International AS and A Level

 Name of student Date Adm. number Year/grade Stream Subject Mechanics 1 (M1) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 Total
Marks 6 6 6 10 10 38
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 5 questions Question 1 Code: 9709/42/O/N/12/2, Topic: - Particles$A$and$B$of masses$m \mathrm{~kg}$and$(1-m) \mathrm{kg}$respectively are attached to the ends of a light inextensible string which passes over a fixed smooth pulley. The system is released from rest with the straight parts of the string vertical. A moves vertically downwards and$0.3$seconds later it has speed$0.6 \mathrm{~m} \mathrm{~s}^{-1}$. Find$\text{(i)}$the acceleration of$A$,$\text{(ii)}$the value of$m$and the tension in the string.$$Question 2 Code: 9709/41/O/N/11/3, Topic: - Three coplanar forces of magnitudes$15 \mathrm{~N}, 12 \mathrm{~N}$and$12 \mathrm{~N}$act at a point$A$in directions as shown in the diagram.$\text{(i)}$Find the component of the resultant of the three forces$\text{(a)}$in the direction of$A B$,$\text{(b)}$perpendicular to$A B$.$\text{(ii)}$Hence find the magnitude and direction of the resultant of the three forces.$$Question 3 Code: 9709/43/O/N/20/4, Topic: - Two small smooth spheres$A$and$B$, of equal radii and of masses$4 \mathrm{~kg}$and$m \mathrm{~kg}$respectively, lie on a smooth horizontal plane. Initially, sphere$B$is at rest and$A$is moving towards$B$with speed$6 \mathrm{~m} \mathrm{~s}^{-1}$. After the collision$A$moves with speed$1.5 \mathrm{~m} \mathrm{~s}^{-1}$and$B$moves with speed$3 \mathrm{~m} \mathrm{~s}^{-1}$. Find the two possible values of the loss of kinetic energy due to the collision.$$Question 4 Code: 9709/43/O/N/18/6, Topic: - A van of mass$3200 \mathrm{~kg}$travels along a horizontal road. The power of the van's engine is constant and equal to$36 \mathrm{~kW}$, and there is a constant resistance to motion acting on the van.$\text{(i)}$When the speed of the van is$20 \mathrm{~m} \mathrm{~s}^{-1}$, its acceleration is$0.2 \mathrm{~m} \mathrm{~s}^{-2}$. Find the resistance force.$$When the van is travelling at$30 \mathrm{~m} \mathrm{~s}^{-1}$, it begins to ascend a hill inclined at$1.5^{\circ}$to the horizontal. The power is increased and the resistance force is still equal to the value found in part$\text{(i)}$.$\text{(ii)}$Find the power required to maintain this speed of$30 \mathrm{~m} \mathrm{~s}^{-1}$.$\text{(iii)}$The engine is now stopped, with the van still travelling at$30 \mathrm{~m} \mathrm{~s}^{-1}$, and the van decelerates to rest. Find the distance the van moves up the hill from the point at which the engine is stopped until it comes to rest.$$Question 5 Code: 9709/41/O/N/12/7, Topic: - A car of mass$1200 \mathrm{~kg}$moves in a straight line along horizontal ground. The resistance to motion of the car is constant and has magnitude$960 \mathrm{~N}$. The car's engine works at a rate of$17280 \mathrm{~W}$.$\text{(i)}$Calculate the acceleration of the car at an instant when its speed is$12 \mathrm{~m} \mathrm{~s}^{-1}$.$$The car passes through the points$A$and$B$. While the car is moving between$A$and$B$it has constant speed$V \mathrm{~m} \mathrm{~s}^{-1}$.$\text{(ii)}$Show that$V=18$.$$At the instant that the car reaches$B$the engine is switched off and subsequently provides no energy. The car continues along the straight line until it comes to rest at the point$C$. The time taken for the car to travel from$A$to$C$is$52.5 \mathrm{~s}$.$\text{(iii)}$Find the distance$A C$.$\$

Worked solutions: P1, P3 & P6 (S1)

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