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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 Start time Duration Stop time

Qtn No. 1 2 3 4 5 Total
Marks 4 5 6 7 9 31
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 5 questions Question 1 Code: 9709/41/O/N/17/1, Topic: - A block of mass$3 \mathrm{~kg}$is initially at rest on a smooth horizontal floor. A force of$12 \mathrm{~N}$, acting at an angle of$25^{\circ}$above the horizontal, is applied to the block. Find the distance travelled by the block in the first 5 seconds of its motion.$[4]$Question 2 Code: 9709/41/O/N/10/2, Topic: - A car of mass$600 \mathrm{~kg}$travels along a horizontal straight road, with its engine working at a rate of$40 \mathrm{~kW}$. The resistance to motion of the car is constant and equal to$800 \mathrm{~N}$. The car passes through the point$A$on the road with speed$25 \mathrm{~m} \mathrm{~s}^{-1}$. The car's acceleration at the point$B$on the road is half its acceleration at$A$. Find the speed of the car at$B$.$[5]$Question 3 Code: 9709/41/O/N/20/4, Topic: - A particle$P$moves in a straight line. It starts from rest at a point$O$on the line and at time$t \mathrm{~s}$after leaving$O$it has acceleration$a \mathrm{~m} \mathrm{~s}^{-2}$, where$a=6 t-18$. Find the distance$P$moves before it comes to instantaneous rest.$[6]$Question 4 Code: 9709/41/O/N/14/5, Topic: - A small block$B$of mass$0.25 \mathrm{~kg}$is attached to the mid-point of a light inextensible string. Particles$P$and$Q$, of masses$0.2 \mathrm{~kg}$and$0.3 \mathrm{~kg}$respectively, are attached to the ends of the string. The string passes over two smooth pulleys fixed at opposite sides of a rough table, with$B$resting in limiting equilibrium on the table between the pulleys and particles$P$and$Q$and block$B$are in the same vertical plane (see diagram).$\text{(i)}$Find the coefficient of friction between$B$and the table.$[3]Q$is now removed so that$P$and$B$begin to move.$\text{(ii)}$Find the acceleration of$P$and the tension in the part$P B$of the string.$[6]$Question 5 Code: 9709/41/O/N/20/6, Topic: - A car of mass$1500 \mathrm{~kg}$is pulling a trailer of mass$750 \mathrm{~kg}$up a straight hill of length$800 \mathrm{~m}$inclined at an angle of$\sin ^{-1} 0.08$to the horizontal. The resistances to the motion of the car and trailer are$400 \mathrm{~N}$and$200 \mathrm{~N}$respectively. The car and trailer are connected by a light rigid tow-bar. The car and trailer have speed$30 \mathrm{~m} \mathrm{~s}^{-1}$at the bottom of the hill and$20 \mathrm{~m} \mathrm{~s}^{-1}$at the top of the hill.$\text{(a)}$Use an energy method to find the constant driving force as the car and trailer travel up the hill.$[5]$After reaching the top of the hill the system consisting of the car and trailer travels along a straight level road. The driving force of the car's engine is$2400 \mathrm{~N}$and the resistances to motion are unchanged.$\text{(b)}$Find the acceleration of the system and the tension in the tow-bar.$[4]\$

Worked solutions: P1, P3 & P6 (S1)

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