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### BOBBYGROOR

#### Cambridge International AS and A Level

 Name of student BOBBYGROOR Date Adm. number Year/grade 1995 Stream Bobbygroor Subject Mechanics 1 (M1) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 10 11 9 10 10 9 59
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/41/M/J/15/6, Topic: - Two particles$A$and$B$start to move at the same instant from a point$O$. The particles move in the same direction along the same straight line. The acceleration of$A$at time$t \mathrm{~s}$after starting to move is$a \mathrm{~m} \mathrm{~s}^{-2}$, where$a=0.05-0.0002 t$.$\text{(i)}$Find$A$'s velocity when$t=200$and when$t=500$.$[4]B$moves with constant acceleration for the first$200 \mathrm{~s}$and has the same velocity as$A$when$t=200. B$moves with constant retardation from$t=200$to$t=500$and has the same velocity as$A$when$t=500$.$\text{(ii)}$Find the distance between$A$and$B$when$t=500$.$[6]$Question 2 Code: 9709/42/M/J/15/6, Topic: - Two particles$P$and$Q$have masses$m \mathrm{~kg}$and$(1-m) \mathrm{kg}$respectively. The particles are attached to the ends of a light inextensible string which passes over a smooth fixed pulley.$P$is held at rest with the string taut and both straight parts of the string vertical.$P$and$Q$are each at a height of$h \mathrm{~m}$above horizontal ground (see Fig. 1).$P$is released and$Q$moves downwards. Subsequently$Q$hits the ground and comes to rest. Fig. 2 shows the velocity-time graph for$P$while$Q$is moving downwards or is at rest on the ground.$\text{(i)}$Find the value of$\mathrm{h}$.$[2]\text{(ii)}$Find the value of$m$, and find also the tension in the string while$Q$is moving.$[6]\text{(iii)}$The string is slack while$Q$is at rest on the ground. Find the total time from the instant that$P$is released until the string becomes taut again.$[3]$Question 3 Code: 9709/43/M/J/15/6, Topic: - A small box of mass$5 \mathrm{~kg}$is pulled at a constant speed of$2.5 \mathrm{~m} \mathrm{~s}^{-1}$down a line of greatest slope of a rough plane inclined at$10^{\circ}$to the horizontal. The pulling force has magnitude$20 \mathrm{~N}$and acts downwards parallel to a line of greatest slope of the plane.$\text{(i)}$Find the coefficient of friction between the box and the plane.$[5]$The pulling force is removed while the box is moving at$2.5 \mathrm{~m} \mathrm{~s}^{-1}$.$\text{(ii)}$Find the distance moved by the box after the instant at which the pulling force is removed. [] Question 4 Code: 9709/41/O/N/15/6, Topic: - A particle$P$moves in a straight line, starting from a point$O$. The velocity of$P$, measured in$\mathrm{m} \mathrm{s}^{-1}$, at time$t \mathrm{~s}$after leaving$O$is given by $$v=0.6 t-0.03 t^{2}$$$\text{(i)}$Verify that, when$t=5$, the particle is$6.25 \mathrm{~m}$from$O$. Find the acceleration of the particle at this time.$[4]\text{(ii)}$Find the values of$t$at which the particle is travelling at half of its maximum velocity.$[6]$Question 5 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.$[6]$When the angle$\theta$is above the horizontal (see Fig. 2) the ring moves.$\text{(ii)}$Find the acceleration of the ring.$[4]$Question 6 Code: 9709/43/O/N/15/6, Topic: - A particle$P$starts from rest at a point$O$of a straight line and moves along the line. The displacement of the particle at time$t \mathrm{~s}$after leaving$O$is$x \mathrm{~m}$, where $$x=0.08 t^{2}-0.0002 t^{3}$$$\text{(i)}$Find the value of$t$when$P$returns to$O$and find the speed of$P$as it passes through$O$on its return.$[4]\text{(ii)}$For the motion of$P$until the instant it returns to$O$, find$\text{(a)}$the total distance travelled,$[3]\text{(b)}$the average speed.$[2]\$

Worked solutions: P1, P3 & P6 (S1)

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