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#### Cambridge International AS and A Level

 Name of student GRADYACIFS Date Adm. number Year/grade 1988 Stream Gradyacifs Subject Mechanics 1 (M1) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 Total
Marks 12 12 10 10 11 55
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 5 questions Question 1 Code: 9709/41/M/J/15/7, Topic: - Particles$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. Particle$A$is held at rest on a rough horizontal table with the string passing over a smooth pulley fixed at the edge of the table. The coefficient of friction between$A$and the table is$0.2$. Particle$B$hangs vertically below the pulley at a height of$0.5 \mathrm{~m}$above the floor (see diagram). The system is released from rest and$0.25 \mathrm{~s}$later the string breaks. A does not reach the pulley in the subsequent motion. Find$\text{(i)}$the speed of$B$immediately before it hits the floor,$\text{(ii)}$the total distance travelled by$A$.$$Question 2 Code: 9709/42/M/J/15/7, Topic: - A small ring$R$is attached to one end of a light inextensible string of length$70 \mathrm{~cm}$. A fixed rough vertical wire passes through the ring. The other end of the string is attached to a point$A$on the wire, vertically above$R$. A horizontal force of magnitude$5.6 \mathrm{~N}$is applied to the point$J$of the string$30 \mathrm{~cm}$from$A$and$40 \mathrm{~cm}$from$R$. The system is in equilibrium with each of the parts$A J$and$J R$of the string taut and angle$A J R$equal to$90^{\circ}$(see diagram).$\text{(i)}$Find the tension in the part$A J$of the string, and find the tension in the part$J R$of the string.$$The ring$R$has mass$0.2 \mathrm{~kg}$and is in limiting equilibrium, on the point of moving up the wire.$\text{(ii)}$Show that the coefficient of friction between$R$and the wire is$0.341$, correct to 3 significant figures.$$A particle of mass$m \mathrm{~kg}$is attached to$R$and$R$is now in limiting equilibrium, on the point of moving down the wire.$\text{(iii)}$Given that the coefficient of friction is unchanged, find the value of$m$.$$Question 3 Code: 9709/41/O/N/15/7, Topic: - A cyclist starts from rest at point$A$and moves in a straight line with acceleration$0.5 \mathrm{~m} \mathrm{~s}^{-2}$for a distance of$36 \mathrm{~m}$. The cyclist then travels at constant speed for$25 \mathrm{~s}$before slowing down, with constant deceleration, to come to rest at point$B$. The distance$A B$is$210 \mathrm{~m}$.$\text{(i)}$Find the total time that the cyclist takes to travel from$A$to$B$.$24 \mathrm{~s}$after the cyclist leaves point$A$, a car starts from rest from point$A$, with constant acceleration$4 \mathrm{~m} \mathrm{~s}^{-2}$, towards$B$. It is given that the car overtakes the cyclist while the cyclist is moving with constant speed.$\text{(ii)}$Find the time that it takes from when the cyclist starts until the car overtakes her.$$Question 4 Code: 9709/42/O/N/15/7, Topic: - A car of mass$1600 \mathrm{~kg}$moves with constant power$14 \mathrm{~kW}$as it travels along a straight horizontal road. The car takes$25 \mathrm{~s}$to travel between two points$A$and$B$on the road.$\text{(i)}$Find the work done by the car's engine while the car travels from$A$to$B$.$$The resistance to the car's motion is constant and equal to$235 \mathrm{~N}$. The car has accelerations at$A$and$B$of$0.5 \mathrm{~m} \mathrm{~s}^{-2}$and$0.25 \mathrm{~m} \mathrm{~s}^{-2}$respectively. Find$\text{(ii)}$the gain in kinetic energy by the car in moving from$A$to$B$,$\text{(iii)}$the distance$A B$.$$Question 5 Code: 9709/43/O/N/15/7, Topic: - A straight hill$A B$has length$400 \mathrm{~m}$with$A$at the top and$B$at the bottom and is inclined at an angle of$4^{\circ}$to the horizontal. A straight horizontal road$B C$has length$750 \mathrm{~m}$. A car of mass$1250 \mathrm{~kg}$has a speed of$5 \mathrm{~m} \mathrm{~s}^{-1}$at$A$when starting to move down the hill. While moving down the hill the resistance to the motion of the car is$2000 \mathrm{~N}$and the driving force is constant. The speed of the car on reaching$B$is$8 \mathrm{~m} \mathrm{~s}^{-1}$.$\text{(i)}$By using work and energy, find the driving force of the car.$$On reaching$B$the car moves along the road$B C$. The driving force is constant and twice that when the car was on the hill. The resistance to the motion of the car continues to be$2000 \mathrm{~N}$. Find$\text{(ii)}$the acceleration of the car while moving from$B$to$C$,$\text{(iii)}$the power of the car's engine as the car reaches$C$.$\$

Worked solutions: P1, P3 & P6 (S1)

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