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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.
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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 $A$, $[2]$

$\text{(ii)}$ the value of $m$ and the tension in the string. $[4]$

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 $A B$.

$[3]$

$\text{(ii)}$ Hence find the magnitude and direction of the resultant of the three forces. $[3]$

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. $[6]$

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. $[3]$

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 $30 \mathrm{~m} \mathrm{~s}^{-1}$. $[3]$

$\text{(iii)}$ 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. $[4]$

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 $12 \mathrm{~m} \mathrm{~s}^{-1}$. $[3]$

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 $V=18$. $[2]$

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 $A C$. $[5]$

Worked solutions: P1, P3 & P6 (S1)

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