A-LevelMathematicsMechanics9709/42 · Feb/Mar 2025 · Q25 Marks

A cyclist is travelling along a straight horizontal road at a speed of 4 ms⁻¹ when she passes a point O. She accelerates at a constant rate for a distance of 42 m, reaching a speed of V ms⁻¹. She maintains the speed of V ms⁻¹ for 50m and then decelerates at 2 ms⁻² before coming to rest. The distance travelled while decelerating is 16m.

(a)Find the value of V.[2]
(b)Find the total time for which she is in motion from the instant that she passes O.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.

B1 For use of constant acceleration to get a correct equation in V only.
B1
M1 For attempt to find an equation in t during acceleration or deceleration or constant speed. Using their V, s=16, a=−2, u=4 . Must lead to a positive t.
M1 For attempt to find an equation in t for the other 2 sections. Using their V, s=16, a=−2, u=4 . Must lead to a positive t.
A1 AWRT 17.3 from correct work

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Feb/Mar 2025 Paper 4 Variant 2, question 2.

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