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### RYAN HART

#### Cambridge International AS and A Level

 Name of student RYAN HART Date Adm. number Year/grade 1990 Stream Ryan Hart Subject Mechanics 1 (M1) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 11 10 10 10 11 10 62
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/41/M/J/11/7, Topic: - Loads$A$and$B$, of masses$1.2 \mathrm{~kg}$and$2.0 \mathrm{~kg}$respectively, are attached to the ends of a light inextensible string which passes over a fixed smooth pulley.$A$is held at rest and$B$hangs freely, with both straight parts of the string vertical.$A$is released and starts to move upwards. It does not reach the pulley in the subsequent motion.$\text{(i)}$Find the acceleration of$A$and the tension in the string.$[4]\text{(ii)}$Find, for the first$1.5$metres of$A$'s motion,$\text{(a)}$A's gain in potential energy,$\text{(b)}$the work done on$A$by the tension in the string,$\text{(c)}$A's gain in kinetic energy.$[3]B$hits the floor$1.6$seconds after$A$is released.$B$comes to rest without rebounding and the string becomes slack.$\text{(iii)}$Find the time from the instant the string becomes slack until it becomes taut again.$[4]$Question 2 Code: 9709/42/M/J/11/7, Topic: - A walker travels along a straight road passing through the points$A$and$B$on the road with speeds$0.9 \mathrm{~m} \mathrm{~s}^{-1}$and$1.3 \mathrm{~m} \mathrm{~s}^{-1}$respectively. The walker's acceleration between$A$and$B$is constant and equal to$0.004 \mathrm{~m} \mathrm{~s}^{-2}$.$\text{(i)}$Find the time taken by the walker to travel from$A$to$B$, and find the distance$A B$.$[3]$A cyclist leaves$A$at the same instant as the walker. She starts from rest and travels along the straight road, passing through$B$at the same instant as the walker. At time$t \mathrm{~s}$after leaving$A$the cyclist's speed is$k t^{3} \mathrm{~m} \mathrm{~s}^{-1}$, where$k$is a constant.$\text{(ii)}$Show that when$t=64.05$the speed of the walker and the speed of the cyclist are the same, correct to 3 significant figures.$[5]\text{(ii)}$Find the cyclist's acceleration at the instant she passes through$B$.$[2]$Question 3 Code: 9709/43/M/J/11/7, Topic: - A particle travels in a straight line from$A$to$B$in$20 \mathrm{~s}$. Its acceleration$t$seconds after leaving$A$is$a \mathrm{~m} \mathrm{~s}^{-2}$, where$\displaystyle a=\frac{3}{160} t^{2}-\frac{1}{800} t^{3}$. It is given that the particle comes to rest at$B$.$\text{(i)}$Show that the initial speed of the particle is zero.$[4]\text{(ii)}$Find the maximum speed of the particle.$[2]\text{(iii)}$Find the distance$A B$.$[4]$Question 4 Code: 9709/41/O/N/11/7, Topic: - A particle$P$starts from a point$O$and moves along a straight line.$P$'s velocity$t$s after leaving$O$is$v \mathrm{~m} \mathrm{~s}^{-1}$, where $$v=0.16 t^{\frac{3}{2}}-0.016 t^{2}$$$P$comes to rest instantaneously at the point$A$.$\text{(i)}$Verify that the value of$t$when$P$is at$A$is 100.$[1]\text{(ii)}$Find the maximum speed of$P$in the interval$0< t <100$.$[4]\text{(iii)}$Find the distance$O A$.$[3]\text{(iv)}$Find the value of$t$when$P$passes through$O$on returning from$A$.$[2]$Question 5 Code: 9709/42/O/N/11/7, Topic: - A tractor travels in a straight line from a point$A$to a point$B$. The velocity of the tractor is$v \mathrm{~m} \mathrm{~s}^{-1}$at time$t \mathrm{~s}$after leaving$A$.$\text{(i)}$The diagram shows an approximate velocity-time graph for the motion of the tractor. The graph consists of two straight line segments. Use the graph to find an approximation for$\text{(a)}$the distance$A B$,$[2]\text{(b)}$the acceleration of the tractor for$0< t <400$and for$400< t <800$.$[2]\text{(ii)}$The actual velocity of the tractor is given by$v=0.04 t-0.00005 t^{2}$for$0 \leqslant t \leqslant 800$.$\text{(a)}$Find the values of$t$for which the actual acceleration of the tractor is given correctly by the approximate velocity-time graph in part$\text{(i)}$.$[3]$For the interval$0 \leqslant t \leqslant 400$, the approximate velocity of the tractor in part$\text{(i)}$is denoted by$v_{1} \mathrm{~m} \mathrm{~s}^{-1}\text{(b)}$Express$v_{1}$in terms of$t$and hence show that$v_{1}-v=0.00005(t-200)^{2}-1$.$[2]\text{(c)}$Deduce that$-1 \leqslant v_{1}-v \leqslant 1$.$[2]$Question 6 Code: 9709/43/O/N/11/7, Topic: - A car of mass$600 \mathrm{~kg}$travels along a straight horizontal road starting from a point$A$. The resistance to motion of the car is$750 \mathrm{~N}$.$\text{(i)}$The car travels from$A$to$B$at constant speed in$100 \mathrm{~s}$. The power supplied by the car's engine is constant and equal to$30 \mathrm{~kW}$. Find the distance$A B$.$[3]\text{(ii)}$The car's engine is switched off at$B$and the car's speed decreases until the car reaches$C$with a speed of$20 \mathrm{~m} \mathrm{~s}^{-1}$. Find the distance$B C$.$[3]\text{(iii)}$The car's engine is switched on at$C$and the power it supplies is constant and equal to$30 \mathrm{~kW}$. The car takes$14 \mathrm{~s}$to travel from$C$to$D$and reaches$D$with a speed of$30 \mathrm{~m} \mathrm{~s}^{-1}$. Find the distance$C D.[4]\$

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