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Chapter 6 Practice Paper: Kinematics — question paper

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QQ/S4AM/CH6

Secondary 4 · Additional Mathematics (G3)

Chapter 6 Practice Paper

Kinematics

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Additional Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 6 (C1 Kinematics: calculus for straight-line motion).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures unless told otherwise. Throughout this paper, displacement s is in metres and time t is in seconds.

  1. 1

    A particle moves along a straight line with displacement s = 3t² − t³.

    1. (a)

      Find an expression for the velocity v.

      [2]
    2. (b)

      Find an expression for the acceleration a.

      a =[1]
    3. (c)

      Find the times at which the particle is at rest.

      [2]
  2. 2

    A particle moves with acceleration a = 4t − 3. Its velocity is 5 m/s and its displacement is 0 when t = 0.

    1. (a)

      Find an expression for v in terms of t.

      [3]
    2. (b)

      Find an expression for s in terms of t.

      [2]
    3. (c)

      Find the velocity when t = 2.

      v =[1]
  3. 3

    A particle moves along a straight line with displacement s = 2t³ − 21t² + 60t for t ≥ 0.

    1. (a)

      Find the times at which the particle is at rest.

      [3]
    2. (b)

      Find the displacement from the start when t = 5.

      s =[1]
    3. (c)

      Find the total distance travelled in the first 5 seconds.

      [3]
  4. 4

    A particle moves with velocity v = 6t − 3t² for 0 ≤ t ≤ 3.

    1. (a)

      Find the maximum velocity and the time at which it occurs, justifying that it is a maximum.

      [3]
    2. (b)

      Find the velocity at the instant the acceleration is zero.

      v =[1]
    3. (c)

      Find the total distance travelled from t = 0 to t = 3.

      [2]
  5. 5

    A particle moves along a straight line with displacement s = t² − 8t + 12 metres from a fixed point O.

    1. (a)

      Write down the displacement of the particle when t = 0.

      s =[1]
    2. (b)

      Find the time at which the particle is instantaneously at rest, and its displacement then.

      [2]
    3. (c)

      Find the total distance travelled in the first 5 seconds.

      [3]

— End of paper —