A-LevelMathematicsMechanics9709/43 · Oct/Nov 2020 · Q510 Marks

A particle P moves in a straight line. It starts at a point O on the line and at time t s after leaving O it has velocity v m s¯¹, where v = 4t² – 20t + 21.

(a)Find the values of t for which P is at instantaneous rest.[2]
(b)Find the initial acceleration of P.[2]
(c)Find the minimum velocity of P.[2]
(d)Find the distance travelled by P during the time when its velocity is negative.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[1] For setting v = 0 and attempting to solve v = 0
[1] t = 1.5 and t = 3.5
[1] For using a = dv/dt and evaluating for t = 0
[1] a = -20
[1] For setting a = 0, attempting to solve for t and substituting to obtain v, or for attempting to complete the square on the expression for v
[1] Vmin = -4 ms-1
[1] For using s = ∫v dt and attempting integration
[1] Correct integration
[1] Substitute their limits (1.5 and 3.5) into their integral
[1] Distance = 16/3 = 5.33 m

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source: A-Level Mathematics, Oct/Nov 2020 Paper 4 Variant 3, question 5.

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