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4024/22 May/Jun 2022, Question 7: Speed-Time Graphs and Acceleration

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 10 marks

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The question, in short

Use a speed–time graph for a cyclist to find acceleration, describe a phase, find T from total distance 558 m, convert 6 m/s, and bound a car's average speed.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 1 mark

Calculate the cyclist's acceleration over the first 8 seconds from the graph.

  1. 1Acceleration = 6 ÷ 8
  2. 2= 0.75 m/s²

Answer0.75 or 3/4 or 6/8

Part (aii) · 1 mark

Describe how the cyclist moves between t = 8 and t = 90.

  1. 1The graph is horizontal, so the cyclist travels at a constant speed of 6 m/s

AnswerTravelling at a constant/uniform speed or Travelling at acceleration of 0

Part (aiii) · 3 marks

Given total distance 558 m, find the value of T.

  1. 1Distance = 1/2 × 8 × 6 + (90 − 8) × 6 + 1/2 × (T − 90) × 6
  2. 2= 24 + 492 + 3(T − 90) = 558
  3. 33(T − 90) = 42, so T − 90 = 14
  4. 4T = 104

Answer104

Part (aiv) · 2 marks

Convert 6 m/s into km/h.

  1. 16 m/s = 6 × 3600 m/h = 21 600 m/h
  2. 221 600 ÷ 1000 = 21.6 km/h

Answer21.6 or 21 3/5

Part (b) · 3 marks

Car travels 352 km (nearest km) in 4.2 hours (nearest 0.1 hour); find the upper bound of average speed.

  1. 1Upper bound of distance = 352.5 km
  2. 2Lower bound of time = 4.15 h
  3. 3Upper bound of speed = 352.5 ÷ 4.15
  4. 4= 84.93… ≈ 84.9 km/h

Answer84.9 or 84.93 to 84.94

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