A-LevelMathematicsMechanics9709/43 · Oct/Nov 2018 · Q35 Marks

A particle of mass 1.2kg moves in a straight line AB. It is projected with speed 7.5 ms¯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 J.

(i)Given that AB is horizontal, find the speed of the particle at B.[2]
(ii)It is given instead that AB is inclined at 30° below the horizontal and that the speed of the particle at B is 9 ms¯¹. The work done against the resistance force remains the same. Find the distance AB.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[M1] For use of KE and 25 in a 3 term equation [½ x 1.2 × 7.5² – ½ × 1.2 × v² = 25]
[A1] v = 3.82 m s¯¹ (3.81881...)
[B1] Correct expression for PE [1.2gdsin30]
[M1] For 4 term work / energy equation [½ x 1.2 × 7.5² – 25 + 1.2gdsin30 = ½ × 1.2 × 9²]
[A1] d = 6.64 m (6.64166...)

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2018 Paper 4 Variant 3, question 3.

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