Practice Paper 4 (Mechanics) (CIE A Level Maths: Probability & Statistics 2)

Practice Paper Questions

1
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4 marks

The displacement of a particle is shown in the displacement-time graph below. Displacement is measured in metres from its starting position and time is measured in seconds.

edexcel-al-maths-mechanics-topic-2-1-e---q1

(i)
Find the displacement of the particle from its starting position after 3 seconds.

(ii)
For how long was the particle stationary?

(iii)
Find the velocity of the particle for the last 5 seconds of its motion.

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2a
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4 marks

Two spheres A and B are of equal radius and have masses 5 space k g and m space k g respectively. A and B are moving in the same direction in a straight line on a smooth horizontal surface when they collide directly. Immediately before the collision, A and B are moving with speeds 12 space m space s to the power of negative 1 end exponent and 2 space m space s to the power of negative 1 end exponent respectively. Immediately after the collision, the speed of A is 2 space m space s to the power of negative 1 end exponent, the speed of B is 4 space m space s to the power of negative 1 end exponent and the direction of motion of B is unchanged.

Find the two possible values of m.

2b
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3 marks

Show that the minimum total kinetic energy lost in the collision is 140 space straight J.

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3
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5 marks

The following force diagram shows three forces acting on a particle:

3-3-v-h-q-1-a-level-maths-mechnics

Given that the resultant force on the particle in the vertical direction is 44.8 N downwards, find the size of the angle theta.  Give your answer in degrees correct to 3 significant figures.

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4a
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3 marks

A particle of mass 12 kg is being pushed up a smooth slope by a force of 50 N that acts horizontally. The slope is inclined at 20° to the horizontal, as shown in the diagram below:

mech-3-3-h-q4

Calculate the acceleration of the particle up the slope.

4b
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3 marks

Calculate the normal reaction force of the slope on the particle.

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5a
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5 marks

A train consisting of an engine and five carriages moves forwards on a straight horizontal track.  The couplings that connect the carriages can be modelled as light and inextensible. A constant resistive force of 2800 N acts on the engine and a constant resistive force of 500 N acts on each of the five carriages.  The maximum speed of the train on the track is 35 m s-1. 

Find the maximum power output of the engine.

5b
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3 marks

Find the maximum acceleration of the train at the instant when it is travelling at a speed of 20 m s-1.  The mass of the engine is 15 tonnes, and the mass of each carriage is 7 tonnes.

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6a
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3 marks

A home-made rocket is launched from rest at ground level with time t equals 0 space seconds.

The acceleration of the rocket, measured in metres per square second, is modelled by the equation

 a equals 40 plus 6 t minus t squared                        t space greater or equal than space 0

(i)
Write down the acceleration of the rocket at launch.

(ii)
Find the acceleration of the rocket after 9 seconds.
6b
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4 marks
(i)
Find an expression for the velocity of the rocket at time t.

(ii)
Find an expression for the displacement of the rocket at time  t.

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7a
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3 marks

A particle moving along a straight line has velocity v space straight m space straight s to the power of negative 1 end exponent, at time t seconds, and its motion is described the equation

v = t24t + 4           

(i)
Write down the initial velocity of the particle.

(ii)
Find the time at which the particle is instantaneously stationary.

7b
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2 marks

Show that the acceleration of the particle is negative for the first 2 seconds of its motion.

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8
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8 marks

Two particles A and B, of masses 2.7 kg and 2.2 kg respectively, are connected by means of a light inextensible string.  Particle A is held motionless on a rough fixed plane inclined at 25° to the horizontal.  The string passes over a smooth light pulley fixed at the top of the plane so that B is hanging vertically downwards as shown in the diagram below:

mech-3-3-h-q9

The string between A and the pulley lies along a line of greatest slope of the plane, and B hangs freely from the pulley.  The coefficient of friction between particle A and the plane is μ.

 

The system is released from rest with the string taut.  Given that particle B descends 1.82 m in the first 3 seconds after it is released, find the value of μ.

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