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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 | Total |
---|---|---|---|---|---|---|---|---|---|---|---|

Marks | 4 | 5 | 6 | 8 | 7 | 7 | 8 | 9 | 11 | 13 | 78 |

Score |

Question 1 Code: 9709/41/M/J/11/1, Topic: -

A car of mass $700 \mathrm{~kg}$ is travelling along a straight horizontal road. The resistance to motion is constant and equal to $600 \mathrm{~N}$.

$\text{(i)}$ Find the driving force of the car's engine at an instant when the acceleration is $2 \mathrm{~m} \mathrm{~s}^{-2}$. $[2]$

$\text{(ii)}$ Given that the car's speed at this instant is $15 \mathrm{~m} \mathrm{~s}^{-1}$, find the rate at which the car's engine is working. $[2]$

Question 2 Code: 9709/41/M/J/16/1, Topic: -

A lift moves upwards from rest and accelerates at $0.9 \mathrm{~m} \mathrm{~s}^{-2}$ for $3 \mathrm{~s}$. The lift then travels for $6 \mathrm{~s}$ at constant speed and finally slows down, with a constant deceleration, stopping in a further $4 \mathrm{~s}$.

$\text{(i)}$ Sketch a velocity-time graph for the motion. $[3]$

$\text{(ii)}$ Find the total distance travelled by the lift. $[2]$

Question 3 Code: 9709/42/M/J/19/1, Topic: -

Coplanar forces of magnitudes $40 \mathrm{~N}, 32 \mathrm{~N}, P \mathrm{~N}$ and $17 \mathrm{~N}$ act at a point in the directions shown in the diagram. The system is in equilibrium. Find the values of $P$ and $\theta$. $[6]$

Question 4 Code: 9709/41/O/N/11/4, Topic: -

$A, B$ and $C$ are three points on a line of greatest slope of a smooth plane inclined at an angle of $\theta^{\circ}$ to the horizontal. $A$ is higher than $B$ and $B$ is higher than $C$, and the distances $A B$ and $B C$ are $1.76 \mathrm{~m}$ and $2.16 \mathrm{~m}$ respectively. A particle slides down the plane with constant acceleration $a \mathrm{~m} \mathrm{~s}^{-2}$. The speed of the particle at $A$ is $u \mathrm{~m} \mathrm{~s}^{-1}$ (see diagram). The particle takes $0.8 \mathrm{~s}$ to travel from $A$ to $B$ and takes $1.4 \mathrm{~s}$ to travel from $A$ to $C$. Find

$\text{(i)}$ the values of $u$ and $a$, $[6]$

$\text{(ii)}$ the value of $\theta$. $[2]$

Question 5 Code: 9709/42/O/N/12/4, Topic: -

Three coplanar forces of magnitudes $68 \mathrm{~N}, 75 \mathrm{~N}$ and $100 \mathrm{~N}$ act at an origin $O$, as shown in the diagram. The components of the three forces in the positive $x$-direction are $-60 \mathrm{~N}, 0 \mathrm{~N}$ and $96 \mathrm{~N}$, respectively. Find

$\text{(i)}$ the components of the three forces in the positive $y$-direction, $[3]$

$\text{(ii)}$ the magnitude and direction of the resultant of the three forces. $[4]$

Question 6 Code: 9709/41/O/N/17/4, Topic: -

The diagram shows the velocity-time graph of a particle which moves in a straight line. The graph consists of 5 straight line segments. The particle starts from rest at a point $A$ at time $t=0$, and initially travels towards point $B$ on the line.

$\text{(i)}$ Show that the acceleration of the particle between $t=3.5$ and $t=6$ is $-10 \mathrm{~m} \mathrm{~s}^{-2}$. $[1]$

$\text{(ii)}$ The acceleration of the particle between $t=6$ and $t=10$ is $7.5 \mathrm{~m} \mathrm{~s}^{-2}$. When $t=10$ the velocity of the particle is $V \mathrm{~m} \mathrm{~s}^{-1}$. Find the value of $V$. $[2]$

$\text{(iii)}$ The particle comes to rest at $B$ at time $T \mathrm{~s}$. Given that the total distance travelled by the particle between $t=0$ and $t=T$ is $100 \mathrm{~m}$, find the value of $T$. $[4]$

Question 7 Code: 9709/41/M/J/14/5, Topic: -

A car of mass $1100 \mathrm{~kg}$ starts from rest at $O$ and travels along a road $O A B.$ The section $O A$ is straight, of length $1760 \mathrm{~m}$, and inclined to the horizontal with $A$ at a height of $160 \mathrm{~m}$ above the level of $O$. The section $A B$ is straight and horizontal (see diagram). While the car is moving the driving force of the car is $1800 \mathrm{~N}$ and the resistance to the car's motion is $700 \mathrm{~N}$. The speed of the car is $v \mathrm{~m} \mathrm{~s}^{-1}$ when the car has travelled a distance of $x \mathrm{~m}$ from $O$.

$\text{(i)}$ For the car's motion from $O$ to $A$, write down its increase in kinetic energy in terms of $v$ and its increase in potential energy in terms of $x$. Hence find the value of $k$ for which $k v^{2}=x$ for $0 \leqslant x \leqslant 1760$. $[4]$

$\text{(ii)}$ Show that $v^{2}=2 x-3200$ for $x \geqslant 1760$. $[4]$

Question 8 Code: 9709/41/O/N/13/6, Topic: -

Particles $A$ and $B$, of masses $0.3 \mathrm{~kg}$ and $0.7 \mathrm{~kg}$ respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley. $A$ is held at rest and $B$ hangs freely, with both straight parts of the string vertical and both particles at a height of $0.52 \mathrm{~m}$ above the floor (see diagram). $A$ is released and both particles start to move.

$\text{(i)}$ Find the tension in the string. $[4]$

When both particles are moving with speed $1.6 \mathrm{~m} \mathrm{~s}^{-1}$ the string breaks.

$\text{(ii)}$ Find the time taken, from the instant that the string breaks, for $A$ to reach the floor. $[5]$

Question 9 Code: 9709/42/M/J/13/7, Topic: -

Particles $A$ of mass $0.26 \mathrm{~kg}$ and $B$ of mass $0.52 \mathrm{~kg}$ are attached to the ends of a light inextensible string. The string passes over a small smooth pulley $P$ which is fixed at the top of a smooth plane. The plane is inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha=\frac{16}{65}$ and $\cos \alpha=\frac{63}{65}. A$ is held at rest at a point $2.5$ metres from $P$, with the part $A P$ of the string parallel to a line of greatest slope of the plane. $B$ hangs freely below $P$ at a point $0.6 \mathrm{~m}$ above the floor (see diagram). $A$ is released and the particles start to move. Find

$\text{(i)}$ the magnitude of the acceleration of the particles and the tension in the string, $[5]$

$\text{(ii)}$ the speed with which $B$ reaches the floor and the distance of $A$ from $P$ when $A$ comes to instantaneous rest. $[6]$

Question 10 Code: 9709/43/M/J/15/7, Topic: -

A particle $P$ moves on a straight line. It starts at a point $O$ on the line and returns to $O 100 \mathrm{~s}$ later. The velocity of $P$ is $v \mathrm{~m} \mathrm{~s}^{-1}$ at time $t \mathrm{~s}$ after leaving $O$, where

$$ v=0.0001 t^{3}-0.015 t^{2}+0.5 t $$$\text{(i)}$ Show that $P$ is instantaneously at rest when $t=0, t=50$ and $t=100$. $[2]$

$\text{(ii)}$ Find the values of $v$ at the times for which the acceleration of $P$ is zero, and sketch the velocitytime graph for $P$ 's motion for $0 \leqslant t \leqslant 100$. $[7]$

$\text{(iii)}$ Find the greatest distance of $P$ from $O$ for $0 \leqslant t \leqslant 100$. $[4]$