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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 Total
Marks 4 5 6 8 7 7 8 9 11 13 78
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 10 questions 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]\$

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