AQA A-Level Physics Paper 1, June 2023: Question 19

1 mark · Medium difficulty · Multiple Choice

Identify the quantities represented by the gradient and the area under a momentum-time graph for an object moving in a straight line.

Practise this question

Question

Multiple choice question 19 asks which quantities can be calculated from the gradient and area under a momentum-time graph for an object moving in a straight line. A table provides four options labeled A to D, listing combinations of 'power', 'force', 'mass times displacement', and 'work done times time' for the gradient and area under the graph.
Question text

19 An object is moving in a straight line. A graph is plotted to show the variation of the

momentum of the object with time.

Which quantities can be calculated from the gradient of the graph and the area under

the graph?

[1 mark]

Gradient of graph Area under graph

A power mass × displacement

B force work done × time

C power work done × time

D force mass × displacement

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer is D, corresponding to force for the gradient and mass times displacement for the area under the graph.

19 D force mass × displacement

How to answer it

Momentum-Time Graph Analysis

What this question tests

This question assesses your understanding of graphical analysis in kinematics and dynamics—specifically, interpreting the physical significance of the gradient and the area under a momentum-time graph using core equations of motion and Newton's laws.

Question 19

Multiple Choice Analysis

✅ Correct Answer: D

The correct option is D (Gradient: force, Area: mass × displacement).

Mark awarded: 1 / 1

💡 Key Knowledge

  • Gradient: Defined as change in y divided by change in time ( Δp / Δt ). By Newton's second law, rate of change of momentum equals force ( F = Δp / Δt ).
  • Area under graph: Defined as momentum multiplied by time ( p × t ). Since momentum p = m × v , this equals m × v × t . Because velocity multiplied by time is displacement ( v × t = s ), the area simplifies to m × s (mass × displacement).

🧠 Exam Technique

When faced with "gradient and area" graph questions:

  1. Write down the quantities on the axes (y-axis: momentum p , x-axis: time t ).
  2. For the gradient, think y / x ( p / t ) and recall physical laws linking these variables.
  3. For the area, think y × x ( p × t ) and substitute definitions ( p = mv ) to simplify the algebraic expression.

❌ Common Errors

  • Confusing momentum-time graphs with velocity-time graphs (where gradient is acceleration and area is displacement).
  • Mistakenly thinking the area under a momentum-time graph gives impulse (impulse is the change in momentum, which relates to the area under a force-time graph, not momentum-time).
  • Failing to break down p × t into m × v × t to recognize that v × t forms displacement s .

Topics

Physics · 3.4 Mechanics and materials

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.