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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 6 7 8 9 10 11 12 Total
Marks 4 5 5 5 6 4 6 6 11 8 8 11 79
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject.
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Question 1 Code: 9709/41/M/J/12/1, Topic: -

A car of mass $880 \mathrm{~kg}$ travels along a straight horizontal road with its engine working at a constant rate of $P \mathrm{~W}$. The resistance to motion is $700 \mathrm{~N}$. At an instant when the car's speed is $16 \mathrm{~m} \mathrm{~s}^{-1}$ its acceleration is $0.625 \mathrm{~m} \mathrm{~s}^{-2}$. Find the value of $P$. $[4]$

Question 2 Code: 9709/43/M/J/17/1, Topic: -

A man pushes a wheelbarrow of mass $25 \mathrm{~kg}$ along a horizontal road with a constant force of magnitude $35 \mathrm{~N}$ at an angle of $20^{\circ}$ below the horizontal. There is a constant resistance to motion of $15 \mathrm{~N}$. The wheelbarrow moves a distance of $12 \mathrm{~m}$ from rest.

$\text{(i)}$ Find the work done by the man. $[2]$

$\text{(ii)}$ Find the speed attained by the wheelbarrow after 12 m. $[3]$

Question 3 Code: 9709/41/M/J/12/2, Topic: -

 

Forces of magnitudes $13 \mathrm{~N}$ and $14 \mathrm{~N}$ act at a point $O$ in the directions shown in the diagram. The resultant of these forces has magnitude $15 \mathrm{~N}$. Find

$\text{(i)}$ the value of $\theta$, $[3]$

$\text{(ii)}$ the component of the resultant in the direction of the force of magnitude $14 \mathrm{~N}$. $[2]$

Question 4 Code: 9709/41/M/J/16/2, Topic: -

A box of mass $25 \mathrm{~kg}$ is pulled, at a constant speed, a distance of $36 \mathrm{~m}$ up a rough plane inclined at an angle of $20^{\circ}$ to the horizontal. The box moves up a line of greatest slope against a constant frictional force of $40 \mathrm{~N}$. The force pulling the box is parallel to the line of greatest slope. Find

$\text{(i)}$ the work done against friction, $[1]$

$\text{(ii)}$ the change in gravitational potential energy of the box, $[2]$

$\text{(iii)}$ the work done by the pulling force. $[2]$

Question 5 Code: 9709/43/M/J/17/3, Topic: -

A train travels between two stations, $A$ and $B$. The train starts from rest at $A$ and accelerates at a constant rate for $T \mathrm{~s}$ until it reaches a speed of $25 \mathrm{~m} \mathrm{~s}^{-1}$. It then travels at this constant speed before decelerating at a constant rate, coming to rest at $B$. The magnitude of the train's deceleration is twice the magnitude of its acceleration. The total time taken for the journey is $180 \mathrm{~s}$.

$\text{(i)}$ Sketch the velocity-time graph for the train's journey from $A$ to $B$. $[1]$

 

$\text{(ii)}$ Find an expression, in terms of $T$, for the length of time for which the train is travelling with constant speed. $[2]$

$\text{(iii)}$ The distance from $A$ to $B$ is $3300 \mathrm{~m}$. Find how far the train travels while it is decelerating. $[3]$

Question 6 Code: 9709/42/M/J/18/3, Topic: -

 

The three coplanar forces shown in the diagram have magnitudes $3 \mathrm{~N}, 2 \mathrm{~N}$ and $P \mathrm{~N}$. Given that the three forces are in equilibrium, find the values of $\theta$ and $P$. $[3]$

Question 7 Code: 9709/41/M/J/17/4, Topic: -

A car of mass $800 \mathrm{~kg}$ is moving up a hill inclined at $\theta^{\circ}$ to the horizontal, where $\sin \theta=0.15$. The initial speed of the car is $8 \mathrm{~m} \mathrm{~s}^{-1}$. Twelve seconds later the car has travelled $120 \mathrm{~m}$ up the hill and has speed $14 \mathrm{~m} \mathrm{~s}^{-1}$

$\text{(i)}$ Find the change in the kinetic energy and the change in gravitational potential energy of the car. $[3]$

$\text{(ii)}$ The engine of the car is working at a constant rate of $32 \mathrm{~kW}$. Find the total work done against the resistive forces during the twelve seconds. $[3]$

Question 8 Code: 9709/43/M/J/18/4, Topic: -

 

Two particles $A$ and $B$, of masses $0.8 \mathrm{~kg}$ and $1.6 \mathrm{~kg}$ respectively, are connected by a light inextensible string. Particle $A$ is placed on a smooth plane inclined at an angle $\theta$ to the horizontal, where $\sin \theta=\frac{3}{5}$. The string passes over a small smooth pulley $P$ fixed at the top of the plane, and $B$ hangs freely (see diagram). The section $A P$ of the string is parallel to a line of greatest slope of the plane. The particles are released from rest with both sections of the string taut. Use an energy method to find the speed of the particles after each particle has moved a distance of $0.5 \mathrm{~m}$, assuming that $A$ has not yet reached the pulley. $[6]$

Question 9 Code: 9709/41/M/J/10/6, Topic: -

 

Particles $A$ and $B$, of masses $0.2 \mathrm{~kg}$ and $0.45 \mathrm{~kg}$ respectively, are connected by a light inextensible string of length $2.8 \mathrm{~m}$. The string passes over a small smooth pulley at the edge of a rough horizontal surface, which is $2 \mathrm{~m}$ above the floor. Particle $A$ is held in contact with the surface at a distance of $2.1 \mathrm{~m}$ from the pulley and particle $B$ hangs freely (see diagram). The coefficient of friction between $A$ and the surface is $0.3$. Particle $A$ is released and the system begins to move.

$\text{(i)}$ Find the acceleration of the particles and show that the speed of $B$ immediately before it hits the floor is $3.95 \mathrm{~m} \mathrm{~s}^{-1}$, correct to 3 significant figures. $[7]$

$\text{(ii)}$ Given that $B$ remains on the floor, find the speed with which $A$ reaches the pulley. $[4]$

Question 10 Code: 9709/42/M/J/16/6, Topic: -

A car of mass $1100 \mathrm{~kg}$ is moving on a road against a constant force of $1550 \mathrm{~N}$ resisting the motion.

$\text{(i)}$ The car moves along a straight horizontal road at a constant speed of $40 \mathrm{~m} \mathrm{~s}^{-1}$.

$\text{(a)}$ Calculate, in $\mathrm{kW}$, the power developed by the engine of the car. $[2]$

$\text{(b)}$ Given that this power is suddenly decreased by $22 \mathrm{~kW}$, find the instantaneous deceleration of the car. $[3]$

$\text{(ii)}$ The car now travels at constant speed up a straight road inclined at $8^{\circ}$ to the horizontal, with the engine working at $80 \mathrm{~kW}$. Assuming the resistance force remains the same, find this constant speed. $[3]$

Question 11 Code: 9709/43/M/J/17/6, Topic: -

A car of mass $1200 \mathrm{~kg}$ is travelling along a horizontal road.

$\text{(i)}$ It is given that there is a constant resistance to motion.

$\text{(a)}$ The engine of the car is working at $16 \mathrm{~kW}$ while the car is travelling at a constant speed of $40 \mathrm{~m} \mathrm{~s}^{-1}$. Find the resistance to motion. $[2]$

$\text{(b)}$ The power is now increased to $22.5 \mathrm{~kW}$. Find the acceleration of the car at the instant it is travelling at a speed of $45 \mathrm{~m} \mathrm{~s}^{-1}$. $[3]$

$\text{(ii)}$ It is given instead that the resistance to motion of the car is $(590+2 v) \mathrm{N}$ when the speed of the car is $v \mathrm{~m} \mathrm{~s}^{-1}$. The car travels at a constant speed with the engine working at $16 \mathrm{~kW}$. Find this speed. $[3]$

Question 12 Code: 9709/43/M/J/14/7, Topic: -

 

A smooth inclined plane of length $160 \mathrm{~cm}$ is fixed with one end at a height of $40 \mathrm{~cm}$ above the other end, which is on horizontal ground. Particles $P$ and $Q$, of masses $0.76 \mathrm{~kg}$ and $0.49 \mathrm{~kg}$ respectively, are attached to the ends of a light inextensible string which passes over a small smooth pulley fixed at the top of the plane. Particle $P$ is held at rest on the same line of greatest slope as the pulley and $Q$ hangs vertically below the pulley at a height of $30 \mathrm{~cm}$ above the ground (see diagram). $P$ is released from rest. It starts to move up the plane and does not reach the pulley. Find

$\text{(i)}$ the acceleration of the particles and the tension in the string before $Q$ reaches the ground, $[4]$

$\text{(ii)}$ the speed with which $Q$ reaches the ground, $[2]$

$\text{(iii)}$ the total distance travelled by $P$ before it comes to instantaneous rest. $[3]$

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