AQA AS Level Physics Paper 2, June 2022: Question 26

1 mark · Medium difficulty · Multiple Choice

Calculate the total kinetic energy of two objects after they collide and remain together, given their initial masses and velocities.

Practise this question

Question

A multiple-choice question stating that object P has a mass of 7500 kg and travels at 12 m/s, while object Q has a mass of 2500 kg and travels at 20 m/s in the same direction. They collide and remain together, and the question asks for the total kinetic energy immediately after the collision. Four options are provided: A) 70 kJ, B) 140 kJ, C) 980 kJ, and D) 2.0 MJ.
Question text

26 Object P has a mass of 7500 kg and travels at 12 m s−1.

Object Q has a mass of 2500 kg and travels at 20 m s−1 in the same direction as P.

P and Q collide and remain together after the collision.

What is the total kinetic energy of P and Q immediately after the collision?

[1 mark]

A 70 kJ

B 140 kJ

C 980 kJ

D 2.0 MJ

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer is C (AO2), corresponding to 980 kJ.

26 C (AO2) 980 kJ

How to answer it

Total Kinetic Energy After a Completely Inelastic Collision

Question 26 • Multiple Choice • 1 Mark

What this question tests

This question assesses your ability to combine two core mechanics principles: the Principle of Conservation of Momentum for a completely inelastic collision (where objects remain together) and the formula for kinetic energy (KE = 0.5 × m × v²). You must determine the combined velocity post-collision before calculating the final total kinetic energy.

Question Breakdown

Part 26 • Finding Total Kinetic Energy Post-Collision

✅ Correct Answer

C (980 kJ)

Awarded for correctly identifying option C as the correct total kinetic energy.

💡 Key Knowledge

  • Conservation of Momentum: Total momentum before collision equals total momentum after collision ( m₁u₁ + m₂u₂ = (m₁ + m₂)v ).
  • Inelastic Collisions: Objects stick together, meaning they share a single common final velocity ( v ).
  • Kinetic Energy: KE = 0.5 × m × v² where mass is in kg and velocity in m s⁻¹.

🧠 Exam Technique

Since this is a 1-mark multiple-choice question, set out your working quickly on your scratch paper:

  1. Calculate initial total momentum.
  2. Rearrange for common velocity v .
  3. Substitute v and total mass into the KE equation.
  4. Check unit conversions (Joules to kiloJoules).

❌ Common Errors

  • Averaging velocities: Assuming the final velocity is just the mean of 12 and 20 m s⁻¹.
  • Calculating initial KE instead: Finding the KE before the collision instead of after.
  • Unit mismatch: Forgetting to divide final Joule values by 1000 to match the kJ options given in the question.

📐 Step-by-Step Calculation Guide

Step 1: Find the total momentum before the collision

Momentum = mass × velocity ( p = mv )

Momentum of P = 7500 kg × 12 m s⁻¹ = 90,000 Ns (or kg m s⁻¹)

Momentum of Q = 2500 kg × 20 m s⁻¹ = 50,000 Ns

Total initial momentum = 90,000 + 50,000 = 140,000 Ns

Step 2: Find the combined velocity ( v ) after collision

Total mass = 7500 kg + 2500 kg = 10,000 kg

Using conservation of momentum: 140,000 = 10,000 × v

Common velocity v = 140,000 / 10,000 = 14 m s⁻¹

Step 3: Calculate the total kinetic energy immediately after

Total KE = 0.5 × total mass × v²

Total KE = 0.5 × 10,000 kg × (14 m s⁻¹)²

Total KE = 5000 × 196 = 980,000 J

Step 4: Convert to kiloJoules (kJ)

Total KE = 980,000 J / 1000 = 980 kJ (Matches Option C)

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.