AQA AS Level Physics Paper 2, June 2023: Question 8

1 mark · Medium difficulty · Multiple Choice

Calculate the final velocity of two objects that stick together after a collision, given their masses and the initial velocity of the moving object.

Practise this question

Question

Multiple choice question 8. An object of mass 0.20 kg moving with initial velocity u collides with a stationary object of mass 0.30 kg, sticking together with no external forces. Four options for the final velocity are given: A 0.40u, B 0.67u, C 1.5u, and D 2.5u.
Question text

08 An object of mass 0.20 kg moves with an initial velocity u. It collides with a stationary

object of mass 0.30 kg.

The objects stick together when they collide.

No external forces act on the objects.

What is the final velocity of the two objects after the collision?

[1 mark]

A 0.40u

B 0.67u

C 1.5u

D 2.5u

Mark scheme

Show the mark scheme Mark scheme for question 8 showing the correct answer is A, corresponding to the final velocity 0.40u.

08 A 0.40u

How to answer it

Inelastic Collision & Momentum

What this question tests

This question assesses your ability to apply the principle of conservation of momentum to a completely inelastic collision (where objects stick together), handling algebraic velocities and combining masses correctly.

Question 08 [1 Mark]

Final Velocity After Collision

✅ Correct Answer

A ( 0.40u )

Mark Scheme: Option A

💡 Key Knowledge

  • Conservation of Momentum: Total momentum before collision equals total momentum after collision ( p_before = p_after ).
  • Inelastic Collisions: When objects stick together, they form a single combined mass ( m₁ + m₂ ) moving with a common final velocity ( v ).

🧠 Exam Technique

Since this is a 1-mark multiple-choice question, set up your equation quickly on your scratch paper. Do not waste time converting units because the mass values can be added directly in kg, and velocity is kept in terms of the variable u .

❌ Common Errors

  • Inverting the mass ratio (e.g., dividing 0.30 by 0.20 ), which gives distractor C ( 1.5u ).
  • Failing to add the masses together for the combined post-collision body, treating the final mass as just one of the objects.

📐 Step-by-Step Calculation

  1. Write down the conservation of momentum formula:
    Total momentum before = Total momentum after
    (m₁ × u₁) + (m₂ × u₂) = (m₁ + m₂) × v
  2. Substitute the given values:
    (0.20 kg × u) + (0.30 kg × 0) = (0.20 kg + 0.30 kg) × v
    0.20u = 0.50 × v
  3. Rearrange to solve for final velocity v :
    v = 0.20u / 0.50
    v = 0.40u

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.