AQA A-Level Physics Paper 1, June 2023: Question 25

1 mark · Medium difficulty · Multiple Choice

Calculate the speed of a 2.0 kg object at t = 1.0 s given a force-time graph showing a force of 10 N from t = 0 to 0.5 s and 20 N from t = 0.5 to 1.0 s.

Practise this question

Question

A multiple-choice question showing a force-time graph for a 2.0 kg object. The graph shows force F in newtons on the vertical axis ranging from 0 to 20, and time t in seconds on the horizontal axis ranging from 0 to 1.0. The force is constant at 10 N from t = 0 to 0.5 s, then jumps to 20 N and remains constant until t = 1.0 s. Below the graph, the question asks for the speed of the object when t = 1.0 s, followed by four multiple-choice options A through D with values 3.75, 5.00, 7.50, and 15.0 m s^-1.
Question text

25 A variable force F acts on an object of mass 2.0 kg. The object is at rest at time t = 0

The graph shows the variation of F with t.

What is the speed of the object when t = 1.0 s?

[1 mark]

A 3.75 m s−1

B 5.00 m s−1

C 7.50 m s−1

D 15.0 m s−1

Mark scheme

Show the mark scheme The mark scheme table shows question number 25 with the correct answer option C, corresponding to a speed of 7.50 m s^-1.

25 C 7.50 m s−1

How to answer it

Determining Speed from a Force-Time Graph

What this question tests

This question assesses your ability to link graphical analysis with Newton's laws of motion. Specifically, it tests your understanding that the area under a force-time graph represents impulse (change in momentum), and how to use mass to convert momentum into velocity.

Question 25 [1 mark]

Full Worked Solution & Breakdown

✅ Correct Answer

C ( 7.50 m s⁻¹ )

Awarded for correctly identifying option C as the right choice.

💡 Key Knowledge

  • Newton's Second Law states that force is the rate of change of momentum: F = Δp / Δt .
  • Rearranging gives impulse: F × Δt = Δp .
  • The area under a force-time graph equals the impulse (change in momentum).
  • Momentum p = m × v , where m is mass and v is velocity.

🧠 Exam Technique

For multiple-choice questions involving graphs, split composite shapes into simpler geometric areas (rectangles) to calculate totals quickly without making arithmetic errors.

📐 Step-by-Step Calculation

  1. Calculate impulse (Area 1 from t = 0 to 0.5 s):
    Area = base × height = 0.5 s × 10 N = 5.0 N s
  2. Calculate impulse (Area 2 from t = 0.5 to 1.0 s):
    Area = base × height = 0.5 s × 20 N = 10.0 N s
  3. Find total impulse (Total Area):
    Total Impulse = 5.0 + 10.0 = 15.0 N s (which equals change in momentum, Δp).
  4. Find speed at t = 1.0 s:
    Since the object starts from rest ( u = 0 ), final momentum equals total impulse.
    v = Δp / m = 15.0 / 2.0 = 7.50 m s⁻¹

❌ Common Errors & Traps

  • Forgetting mass: Stopping after calculating the total impulse (15.0) and incorrectly selecting option D.
  • Misreading graph values: Taking the height of the second section as 10 N instead of reading the correct grid line value of 20 N.
  • Averaging forces: Incorrectly attempting to find a mean force instead of treating the graph as two distinct rectangular sections.

Topics

Physics · Practical skills · 3.4 Mechanics and materials · Data analysis

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.