A-LevelMathematicsMechanics9709/41 · May/June 2022 · Q16 Marks

A car starts from rest and moves in a straight line with constant acceleration for a distance of 200m, reaching a speed of 25 ms¯¹. The car then travels at this speed for 400 m, before decelerating uniformly to rest over a period of 5 s.

(a)Find the time for which the car is accelerating.[2]
(b)Sketch the velocity-time graph for the motion of the car, showing the key points.[2]
(c)Find the average speed of the car during its motion.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

[M1] For use of s = (u+v)/2 * t or other complete method to find t
[A1] t = 16s
[B1] Through (0, 0) and positive t-axis
[B1] FT their value of t from part (a) (t +16 + 5)
[M1] Total distance = 200+400+1/2*25*5 [= 662.5] (Or trapezium 1/2*25(16+37)[= 662.5]) (Or 200+400+(25+0)/2 * 5)
[A1] Average speed = 662.5/37 = 17.9 ms¯¹ (3 s.f.) (Allow 1325/74 = 17 67/74)

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, May/June 2022 Paper 4 Variant 1, question 1.

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