AQA AS Level Physics Paper 2, June 2025: Question 19

✅ Correct Answer

B: the change in momentum of the object.

💡 Key Knowledge

• Newton's Second Law: Resultant force is defined as the rate of change of momentum:
  F = Δp / Δt
• Impulse: Rearranging gives:
  Impulse = F Δt = Δp
• On any graph where the axes are y and x , the area under the line is given by the integral ∫ y dx . For a force–time graph:
  Area = ∫ F dt = Impulse = Δ(mv)
• Units check: Force × time has units of N s , which simplifies to kg m s⁻¹ (the base unit of momentum).

📐 Dimensional & Physical Analysis

1. Identify graph axes: The vertical axis is Force ( F in N) and the horizontal axis is time ( t in s).
2. Multiply the quantities: Area represents the product of the two axes:
   Area ≈ Force × time
3. Relate to physical definitions:
   F = m × a = m × (Δv / Δt) = Δp / Δt
   F × Δt = Δp (change in momentum).
4. Conclusion: The area under the curve between any two times represents the total impulse delivered, which equals the net change in momentum Δp .

🧠 Exam Technique: "Multiply or Divide?"

When asked what an area or gradient represents, use this quick two-second check:

• Area under graph: Multiply the units of the axes.
  N × s = (kg m s⁻²) × s = kg m s⁻¹ → Momentum!
• Gradient of line: Divide vertical units by horizontal units.
  N / s = kg m s⁻³ → Rate of change of force.

❌ Why the Distractors are Incorrect

• Option A (change in kinetic energy): The area under a Force–displacement ( F–s ) graph represents work done ( W = Fs ), which equals change in kinetic energy, not a Force–time graph.
• Option C (distance travelled): Distance travelled is the area under a velocity–time ( v–t ) graph ( s = vt ).
• Option D (total force that acted): Force is already represented by the vertical axis value. Area multiplies force by time, so it cannot represent force.