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### MIKE GREEN

#### Cambridge International AS and A Level

 Name of student MIKE GREEN Date Adm. number Year/grade 1998 Stream Mike Green Subject Mechanics 1 (M1) Variant(s) P41, P42, P43 Start time Duration Stop time

Qtn No. 1 2 3 4 5 6 Total
Marks 6 4 6 5 7 5 33
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 6 questions Question 1 Code: 9709/41/M/J/18/3, Topic: - A particle$P$of mass$8 \mathrm{~kg}$is on a smooth plane inclined at an angle of$30^{\circ}$to the horizontal. A force of magnitude$100 \mathrm{~N}$, making an angle of$\theta^{\circ}$with a line of greatest slope and lying in the vertical plane containing the line of greatest slope, acts on$P$(see diagram).$\text{(i)}$Given that$P$is in equilibrium, show that$\theta=66.4$, correct to 1 decimal place, and find the normal reaction between the plane and$P$.$\text{(ii)}$Given instead that$\theta=30$, find the acceleration of$P$.$$Question 2 Code: 9709/42/M/J/18/3, Topic: - The three coplanar forces shown in the diagram have magnitudes$3 \mathrm{~N}, 2 \mathrm{~N}$and$P \mathrm{~N}$. Given that the three forces are in equilibrium, find the values of$\theta$and$P$.$$Question 3 Code: 9709/43/M/J/18/3, Topic: - Coplanar forces of magnitudes$8 \mathrm{~N}, 12 \mathrm{~N}$and$18 \mathrm{~N}$act at a point in the directions shown in the diagram. Find the magnitude and direction of the single additional force acting at the same point which will produce equilibrium.$$Question 4 Code: 9709/41/O/N/18/3, Topic: - A van of mass$2500 \mathrm{~kg}$descends a hill of length$0.4 \mathrm{~km}$inclined at$4^{\circ}$to the horizontal. There is a constant resistance to motion of$600 \mathrm{~N}$and the speed of the van increases from$20 \mathrm{~m} \mathrm{~s}^{-1}$to$30 \mathrm{~m} \mathrm{~s}^{-1}$as it descends the hill. Find the work done by the van's engine as it descends the hill.$$Question 5 Code: 9709/42/O/N/18/3, Topic: - The velocity of a particle moving in a straight line is$v \mathrm{~m} \mathrm{~s}^{-1}$at time$t$seconds. The diagram shows a velocity-time graph which models the motion of the particle from$t=0$to$t=T$. The graph consists of four straight line segments. The particle reaches its maximum velocity$V \mathrm{~m} \mathrm{~s}^{-1}$at$t=10$.$\text{(i)}$Find the acceleration of the particle during the first 2 seconds.$\text{(ii)}$Find the value of$V$.$$At$t=6$, the particle is instantaneously at rest at the point$A$. At$t=T$, the particle comes to rest at the point$B.$At$t=0$the particle starts from rest at a point one third of the way from$A$to$B$.$\text{(iii)}$Find the distance$A B$and hence find the value of$T$.$$Question 6 Code: 9709/43/O/N/18/3, Topic: - A particle of mass$1.2 \mathrm{~kg}$moves in a straight line$A B$. It is projected with speed$7.5 \mathrm{~m} \mathrm{~s}^{-1}$from$A$towards$B$and experiences a resistance force. The work done against this resistance force in moving from$A$to$B$is$25 \mathrm{~J}$.$\text{(i)}$Given that$A B$is horizontal, find the speed of the particle at$B$.$\text{(ii)}$It is given instead that$A B$is inclined at$30^{\circ}$below the horizontal and that the speed of the particle at$B$is$9 \mathrm{~ms}^{-1}$. The work done against the resistance force remains the same. Find the distance$A B$.$\$

Worked solutions: P1, P3 & P6 (S1)

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