AQA AS Level Physics Paper 2, November 2021: Question 10

1 mark · Medium difficulty · Multiple Choice

Determine the new speed of an electron whose kinetic energy is doubled, given its initial speed is v.

Practise this question

Question

Multiple-choice question 10 asking for the new speed of an electron whose kinetic energy is doubled. Four options are listed: A, v over the square root of 2; B, square root of 2 times v; C, 2v; D, 4v.
Question text

10 An electron has speed v. The electron’s kinetic energy is doubled.

What is the new speed of the electron?

[1 mark]

v

A

B 2v

C 2v

D 4v

Mark scheme

Show the mark scheme The mark scheme table shows that question 10 corresponds to option B, with the correct answer being the square root of 2 times v.

10 B 2v

How to answer it

Relating Electron Kinetic Energy to Speed

What this question tests

This question assesses your understanding of the relationship between kinetic energy and speed for a particle (specifically an electron) using proportionality and algebraic scaling. You are required to manipulate standard physics equations without inserting numerical values.

Question 10 (Multiple Choice)

Scaling Kinetic Energy and Speed

✅ Correct Answer: B

The correct option is B ( √2v ). Doubling the kinetic energy increases the speed by a factor of the square root of 2.

💡 Key Knowledge

  • The standard formula for kinetic energy is E_k = 0.5 m v² .
  • Since mass ( m ) and the constant 0.5 remain unchanged, kinetic energy is directly proportional to the square of the speed ( E_k ∝ v² ).

🧠 Exam Technique

When dealing with "proportionality scaling" multiple-choice questions, set up a ratio equation comparing the initial state to the final state rather than plugging in random numbers. This prevents careless algebraic flips.

❌ Common Errors

Many students incorrectly choose option C ( 2v ). This happens because they mistakenly assume kinetic energy is directly proportional to speed itself ( E_k ∝ v ) instead of velocity squared ( v² ).

📐 Step-by-Step Derivation

  1. Write out the initial equation:
    E_k = 0.5 m v²
  2. Set up the scaled relationship:
    Let the new kinetic energy be 2E_k and the new speed be v_new .
    2E_k = 0.5 m (v_new)²
  3. Compare equations (divide new by old):
    2 = (v_new / v)²
  4. Rearrange to solve for v_new :
    v_new / v = √2
    v_new = √2 v
Mark allocation: [1 mark] awarded for selecting option B.

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, November 2021. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.