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A-LevelMathematicsMechanics9709/42 · Feb/Mar 2020 · Q710 Marks

A particle moves in a straight line through the point O. The displacement of the particle from O at time t s is s m, where s = t² - 3t + 2 for 0 ≤ t ≤ 6, s = 24/t - t²/4 + 25 for t ≥ 6.

  1. (a)Find the value of t when the particle is instantaneously at rest during the first 6 seconds of its motion.[2]
  2. (b)Find the velocity with which the particle arrives at P and also the velocity with which the particle leaves P.[3]
  3. (c)Find the total distance travelled by the particle in the first 10 seconds of its motion.[5]

Mark scheme

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

  1. [M1] For differentiation of s for 0 ≤ t ≤ 6
  2. [A1]
  3. [B1] t = 6 used in v
  4. [M1] For differentiation of s for t ≥ 6
  5. [A1] Allow v = –11/3
  6. [B1] SOI
  7. [B1] SOI
  8. [B1] SOI
  9. [M1] Evidence of distance rather than displacement involving all three sections, (0, 1.5), (1.5, 6) and (6, 10)
  10. [A1]

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About this question

Topic
Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source
A-Level Mathematics, Feb/Mar 2020 Paper 4 Variant 2, question 7.

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