StudentAid
HomeLearn
9th Class10th Class11th Class12th ClassCambridge past papersBrowse everything
Attendance
Class attendanceVisitor register
For schoolsFor driversFor parentsBook a demo
Learn/ A Level Mathematics/ Past Papers/ 2020/ Oct/Nov 2020 /Paper 4 (Variant 3)

Mechanics — Variant 3

A Level Mathematics · 9709/43 · Oct/Nov 2020

Question Paper

PDF · 108 KB · 12 pages

Mark Scheme

PDF · 278 KB · 11 pages

This browser cannot show the PDF inline.

Open the question paper · Open the mark scheme

Questions

6 of 7 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

1
A particle PP is projected vertically upwards with speed vv m s−1\text{m s}^{-1} from a point on the ground. PP reaches its greatest height after 33 s.
1(a) [1]
Find vv.
1(b) [2]
Find the greatest height of PP above the ground.
2
A box of mass 55 kg is pulled at a constant speed a distance of 1515 m up a rough plane inclined at an angle of 20∘20^\circ to the horizontal. The box moves along a line of greatest slope against a frictional force of 4040 N. The force pulling the box is parallel to the line of greatest slope.
2(a) [1]
Find the work done against friction.
2(b) [2]
Find the change in gravitational potential energy of the box.
2(c) [1]
Find the work done by the pulling force.
3
A string is attached to a block of mass 44 kg which rests in limiting equilibrium on a rough horizontal table. The string makes an angle of 24∘24^\circ above the horizontal and the tension in the string is 3030 N.
3(a) [1]
Draw a diagram showing all the forces acting on the block.
3(b) [5]
Find the coefficient of friction between the block and the table.
4 [6]
Two small smooth spheres AA and BB, of equal radii and of masses 44 kg and mm kg respectively, lie on a smooth horizontal plane. Initially, sphere BB is at rest and AA is moving towards BB with speed 66 m s−1\text{m s}^{-1}. After the collision AA moves with speed 1.51.5 m s−1\text{m s}^{-1} and BB moves with speed 33 m s−1\text{m s}^{-1}. Find the two possible values of the loss of kinetic energy due to the collision.
5
A particle PP moves in a straight line. It starts at a point OO on the line and at time tt s after leaving OO it has velocity vv m s−1\text{m s}^{-1}, where v=4t2−20t+21v = 4t^{2} - 20t + 21.
5(a) [2]
Find the values of tt for which PP is at instantaneous rest.
5(b) [2]
Find the initial acceleration of PP.
5(c) [2]
Find the minimum velocity of PP.
5(d) [4]
Find the distance travelled by PP during the time when its velocity is negative.
6
A car of mass 16001600 kg is pulling a caravan of mass 800800 kg. The car and the caravan are connected by a light rigid tow-bar. The resistances to the motion of the car and caravan are 400400 N and 250250 N respectively.
6(a)
The car and caravan are travelling along a straight horizontal road.
6(a)(i) [2]
Given that the car and caravan have a constant speed of 2525 m s−1\text{m s}^{-1}, find the power of the car's engine.
6(a)(ii) [5]
The engine's power is now suddenly increased to 3939 kW. Find the instantaneous acceleration of the car and caravan and find the tension in the tow-bar.
6(b) [3]
The car and caravan now travel up a straight hill, inclined at an angle of sin⁡−10.05\sin^{-1} 0.05 to the horizontal, at a constant speed of vv m s−1\text{m s}^{-1}. The car's engine is working at 32.532.5 kW. Find vv.

Published by Cambridge Assessment International Education. Reproduced for study use.