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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 3 6 5 5 6 6 8 6 10 8 8 75
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 12 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$2 \mathrm{~m} \mathrm{~s}^{-2}$.$\text{(ii)}$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.$$Question 2 Code: 9709/42/O/N/13/1, Topic: - A small block of weight$5.1 \mathrm{~N}$rests on a smooth plane inclined at an angle$\alpha$to the horizontal, where$\sin \alpha=\frac{8}{17}$. The block is held in equilibrium by means of a light inextensible string. The string makes an angle$\beta$above the line of greatest slope on which the block rests, where$\sin \beta=\frac{7}{25}$(see diagram). Find the tension in the string.$$Question 3 Code: 9709/43/M/J/19/2, Topic: - Coplanar forces of magnitudes$12 \mathrm{~N}, 24 \mathrm{~N}$and$30 \mathrm{~N}$act at a point in the directions shown in the diagram.$\text{(i)}$Find the components of the resultant of the three forces in the$x$-direction and in the$y$-direction.$$Component in$x$-direction. Component in$y$-direction.$\text{(ii)}$Hence find the direction of the resultant.$$Question 4 Code: 9709/41/M/J/20/2, Topic: - A car of mass$1800 \mathrm{~kg}$is towing a trailer of mass$400 \mathrm{~kg}$along a straight horizontal road. The car and trailer are connected by a light rigid tow-bar. The car is accelerating at$1.5 \mathrm{~m} \mathrm{~s}^{-2}.$There are constant resistance forces of$250 \mathrm{~N}$on the car and$100 \mathrm{~N}$on the trailer.$\text{(a)}$Find the tension in the tow-bar.$\text{(b)}$Find the power of the engine of the car at the instant when the speed is$20 \mathrm{~m} \mathrm{~s}^{-1}$.$$Question 5 Code: 9709/42/O/N/20/3, Topic: - A block of mass$m \mathrm{~kg}$is held in equilibrium below a horizontal ceiling by two strings, as shown in the diagram. One of the strings is inclined at$45^{\circ}$to the horizontal and the tension in this string is$T \mathrm{~N}$. The other string is inclined at$60^{\circ}$to the horizontal and the tension in this string is$20 \mathrm{~N}$. Find$T$and$m$.$$Question 6 Code: 9709/41/M/J/16/4, Topic: - Coplanar forces of magnitudes$50 \mathrm{~N}, 48 \mathrm{~N}, 14 \mathrm{~N}$and$P \mathrm{~N}$act at a point in the directions shown in the diagram. The system is in equilibrium. Given that tan$\alpha=\frac{7}{24}$, find the values of$P$and$\theta$.$$Question 7 Code: 9709/42/O/N/16/4, Topic: - A girl on a sledge starts, with a speed of$5 \mathrm{~m} \mathrm{~s}^{-1}$, at the top of a slope of length$100 \mathrm{~m}$which is at an angle of$20^{\circ}$to the horizontal. The sledge slides directly down the slope.$\text{(i)}$Given that there is no resistance to the sledge's motion, find the speed of the sledge at the bottom of the slope.$\text{(ii)}$It is given instead that the sledge experiences a resistance to motion such that the total work done against the resistance is$8500 \mathrm{~J}$, and the speed of the sledge at the bottom of the slope is$21 \mathrm{~m} \mathrm{~s}^{-1}$. Find the total mass of the girl and the sledge.$$Question 8 Code: 9709/43/M/J/13/5, Topic: - A particle$P$is projected vertically upwards from a point on the ground with speed$17 \mathrm{~m} \mathrm{~s}^{-1}$. Another particle$Q$is projected vertically upwards from the same point with speed$7 \mathrm{~ms}^{-1}$. Particle$Q$is projected$T$seconds later than particle$P$.$\text{(i)}$Given that the particles reach the ground at the same instant, find the value of$T$.$\text{(ii)}$At a certain instant when both$P$and$Q$are in motion,$P$is$5 \mathrm{~m}$higher than$Q.$Find the magnitude and direction of the velocity of each of the particles at this instant.$$Question 9 Code: 9709/42/M/J/15/5, Topic: - A particle$P$starts from rest at a point$O$on a horizontal straight line.$P$moves along the line with constant acceleration and reaches a point$A$on the line with a speed of$30 \mathrm{~m} \mathrm{~s}^{-1}$. At the instant that$P$leaves$O$, a particle$Q$is projected vertically upwards from the point$A$with a speed of$20 \mathrm{~m} \mathrm{~s}^{-1}$. Subsequently$P$and$Q$collide at$A$. Find$\text{(i)}$the acceleration of$P$,$\text{(ii)}$the distance$O A$.$$Question 10 Code: 9709/42/O/N/15/6, Topic: - A small ring of mass$0.024 \mathrm{~kg}$is threaded on a fixed rough horizontal rod. A light inextensible string is attached to the ring and the string is pulled with a force of magnitude$0.195 \mathrm{~N}$at an angle of$\theta$with the horizontal, where$\sin \theta=\frac{5}{13}$. When the angle$\theta$is below the horizontal (see Fig. 1) the ring is in limiting equilibrium.$\text{(i)}$Find the coefficient of friction between the ring and the rod.$$When the angle$\theta$is above the horizontal (see Fig. 2) the ring moves.$\text{(ii)}$Find the acceleration of the ring.$$Question 11 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.$\text{(b)}$Given that this power is suddenly decreased by$22 \mathrm{~kW}$, find the instantaneous deceleration of the car.$\text{(ii)}$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.$$Question 12 Code: 9709/42/O/N/18/6, Topic: - A car of mass$1200 \mathrm{~kg}$is driving along a straight horizontal road at a constant speed of$15 \mathrm{~m} \mathrm{~s}^{-1}$. There is a constant resistance to motion of$350 \mathrm{~N}$.$\text{(i)}$Find the power of the car's engine.$$The car comes to a hill inclined at$1^{\circ}$to the horizontal, still travelling at$15 \mathrm{~m} \mathrm{~s}^{-1}$.$\text{(ii)}$The car starts to descend the hill with reduced power and with an acceleration of$0.12 \mathrm{~m} \mathrm{~s}^{-2}$. Given that there is no change in the resistance force, find the new power of the car's engine at the instant when it starts to descend the hill.$\text{(iii)}$When the car is travelling at$20 \mathrm{~m} \mathrm{~s}^{-1}$down the hill, the power is cut off and the car gradually slows down. Assuming that the resistance force remains$350 \mathrm{~N}$, find the distance travelled from the moment when the power is cut off until the speed of the car is reduced to$18 \mathrm{~m} \mathrm{~s}^{-1}$.$\$

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