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/ 2021/ Oct/Nov 2021 /Paper 4 (Variant 2)

Mechanics — Variant 2

A Level Mathematics · 9709/42 · Oct/Nov 2021

Question Paper

PDF · 120 KB · 12 pages

Mark Scheme

PDF · 346 KB · 14 pages

This browser cannot show the PDF inline.

Open the question paper · Open the mark scheme

Questions

2 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.

4
A cyclist starts from rest at a point AA and travels along a straight road ABAB, coming to rest at BB. The displacement of the cyclist from AA at time tt s after the start is ss m, where s=0.004(75t2−t3)s = 0.004(75t^{2} - t^{3}).
4(a) [4]
Show that the distance ABAB is 250250 m.
4(b) [3]
Find the maximum velocity of the cyclist.
5
A railway engine of mass 75 00075\,000 kg is moving up a straight hill inclined at an angle α\alpha to the horizontal, where sin⁡α=0.01\sin \alpha = 0.01. The engine is travelling at a constant speed of 3030 m s−1\text{m s}^{-1}. The engine is working at 960960 kW. There is a constant force resisting the motion of the engine.
5(a) [3]
Find the resistance force. The engine comes to a section of track which is horizontal. At the start of the section the engine is travelling at 3030 m s−1\text{m s}^{-1} and the power of the engine is now reduced to 900900 kW. The resistance to motion is no longer constant, but in the next 6060 s the work done against the resistance force is 46 50046\,500 kJ.
5(b) [4]
Find the speed of the engine at the end of the 6060 s.

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