A sprinter accelerates uniformly from rest and reaches a maximum velocity of 11 m s⁻¹ at the end of the first 4.0 s of a race. The sprinter then maintains this maximum velocity for the remainder of the race. Explain how the gradient of a displacement–time graph for this sprinter would differ between the first 4.0 s and the period after 4.0 s, and describe the shape of the displacement–time graph during each phase.

IB DP Physics Higher Level (2023 syllabus) — A.1 Kinematics · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (4 marks)

During the first 4.0 s the gradient of the displacement–time graph is not constant – it increases from zero as the sprinter accelerates. The gradient at any instant equals the instantaneous velocity, so an increasing gradient shows the sprinter’s velocity is rising. After 4.0 s the sprinter runs at constant speed, so the gradient becomes constant – it no longer changes. The displacement–time graph is therefore a concave‑upward curve in the first 4.0 s and a straight line with a steeper, positive slope for the remainder of the race.

Examiner tips

  • Use the term ‘gradient’ and explain it equals instantaneous velocity; mention ‘increasing gradient’ for acceleration phase.
  • State clearly that the gradient is constant after 4 s and that the graph changes from a curve to a straight line.
  • Include the shape descriptors – concave upward for the first phase, straight line for the second.
  • Use UK spelling (e.g. ‘slope’).

Common mistakes

  • Confusing gradient with slope of the graph; not recognising that gradient equals velocity.
  • Describing the first 4 s as a straight line or saying the gradient is constant throughout.
  • Using the wrong shape terminology (e.g. ‘concave downward’).

Mark scheme (4 marks)

  1. During the first 4.0 s the gradient of the displacement–time graph increases (from zero) / the gradient is not constant.
  2. The gradient equals the instantaneous velocity, so an increasing gradient reflects the increasing velocity / acceleration of the sprinter during this phase.
  3. After 4.0 s the gradient is constant / the gradient does not change.
  4. The shape of the graph is a curve (concave upward / increasing slope) during the first 4.0 s and a straight line with a steeper/positive gradient after 4.0 s.

Key terms in this question

displacement–time graph · gradient

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