AQA GCSE Combined Science: Trilogy Physics Paper 2 (Higher), 2021: Question 6

11 marks · Standard Demand difficulty · Extended Answer

Explain why an aeroplane accelerating at maximum power does not have constant acceleration, and calculate the mass of a hypersonic aeroplane using change in speed, time and resultant force.

Practise this question

Question

The question page shows Question 06 about a hypersonic aeroplane. Part 06.1 states that an aeroplane accelerates from a low speed to a high speed with the engines at maximum power and asks students to explain why the acceleration is not constant for 5 marks, with lined space for an extended written answer. Part 06.2 states that the aeroplane has jet engines and a rocket engine, gives Mach 1 = 330 m/s, says the jet engines accelerate the plane to Mach 5.5 and the rocket engine from Mach 5.5 to Mach 25.5 in 300 s, and gives an average resultant force of 630000 N; it asks students to calculate the mass of the aeroplane to 2 significant figures for 6 marks, with answer lines and a final blank labelled mass in kg.
Question text

06 Scientists are developing a hypersonic aeroplane that will travel much faster than

normal aeroplanes.

06.1 An aeroplane accelerates from a low speed to a high speed with the engines at

maximum power.

Explain why the acceleration is not constant.

[5 marks]

06.2 The hypersonic aeroplane will have jet engines and a rocket engine.

The speed of aeroplanes can be measured on a uniform scale called the Mach scale.

Mach 1 = 330 m/s

The jet engines will accelerate the aeroplane to Mach 5.5.

The rocket engine will accelerate the aeroplane from Mach 5.5 to Mach 25.5 in 300 s.

The average resultant force on the aeroplane when the rocket engine is used

will be 630 000 N.

Calculate the mass of the hypersonic aeroplane.

Give your answer to 2 significant figures.

[6 marks]

Mass (2 significant figures) = kg

Mark scheme

Show the mark scheme The mark scheme is presented in a table with columns for Question, Answers, Extra information, Mark and AO/Spec. For 06.1, marking points state that at maximum power the engine force is constant, air resistance increases as speed increases, resultant force equals engine force minus air resistance, the resultant force therefore decreases, and acceleration is directly proportional to resultant force. For 06.2, the scheme shows delta v = (25.5 minus 5.5) times 330, acceleration calculated as change in velocity divided by 300 giving 22 m/s squared, then mass found from 630000 divided by 22 to give 28636.36 kg and finally 29000 kg to 2 significant figures, with notes allowing correct substitutions and consequential marking.

AO /

Question Answers Extra information Mark

Spec.

06.1 at maximum power the forward 1 AO3

force of the engines is constant

as it accelerates the air resistance 1 AO1

increases

resultant force = force from engines 1 AO1

– air resistance

therefore resultant force decreases 1 AO3

acceleration is directly proportional 1 AO1

to resultant force

6.5.1.4

6.5.4.2.2

6.5.4.1.5

06.2 Δv = (25.5 – 5.5) × 330 allow 6600 m/s 1 AO2

6.5.4.1.5

6.5.5.1

((25.5 ×330) - (5.5 ×330)) allow a correct substitution 1

a =

300 using incorrectly / not

converted values of u and v

allow a correct calculation 1

a = 22 m/s2

using incorrectly / not

converted values of u and v

a = Δv / t must have been

used to score subsequent

marks

allow a correct substitution 1

m = 630 000 / 22 using an incorrectly

calculated value of a

allow a correct calculation 1

m = 28636.36 (kg) using an incorrectly

calculated value of a

this mark can only be 1

m = 29000 (kg) 15

awarded for a calculation

using the correct equations

Total 11

How to answer it

High Demand

Hypersonic Aeroplane: Acceleration and Mass

What this question tests

You need to explain why acceleration changes when forces change, and then use force = mass × acceleration with speeds in m/s to calculate a mass. The question checks your understanding of resultant force, air resistance, unit conversion, and multi-step calculations with correct rounding to 2 significant figures.

Part (a) 06.1 — Why is the acceleration not constant? [5 marks]

✅ Correct answer

  • At maximum power, the forward force from the engines is constant.
  • As the aeroplane speeds up, air resistance increases.
  • Resultant force = force from engines − air resistance.
  • So the resultant force decreases as the plane gets faster.
  • Since acceleration is directly proportional to resultant force, the acceleration decreases, so it is not constant.

💡 Key knowledge

  • Resultant force is the overall force after all forces are combined.
  • If one force stays the same but the opposing force increases, the resultant force gets smaller.
  • Newton’s second law links force and acceleration: bigger resultant force gives bigger acceleration.

🧠 Exam technique

  • Use a chain of reasoning: constant engine force → increasing drag → smaller resultant force → smaller acceleration.
  • The examiner was looking for the idea that the forces are changing, not just “because speed changes”.
  • Top answers clearly linked resultant force to acceleration.

❌ Common errors

  • Saying “acceleration changes because the engine is weaker” — the mark scheme says the engine force is constant at maximum power.
  • Only mentioning air resistance without explaining the effect on resultant force.
  • Saying “speed and acceleration are the same” — they are different quantities.
How the 5 marks are awarded: one mark each for the key steps: constant engine force, increasing air resistance, resultant force equation, decreasing resultant force, and acceleration linked to resultant force.

Part (b) 06.2 — Calculate the mass of the aeroplane [6 marks]

💡 Key knowledge

  • Mach 1 = 330 m/s
  • Speed at Mach 5.5 = 5.5 × 330
  • Speed at Mach 25.5 = 25.5 × 330
  • Use force = mass × acceleration so mass = force ÷ acceleration

📐 Calculations: step by step

  1. Find the change in speed
    Δv = (25.5 − 5.5) × 330
    Δv = 20 × 330 = 6600 m/s
  2. Find the acceleration
    a = Δv ÷ t
    a = 6600 ÷ 300 = 22 m/s²
  3. Use force = mass × acceleration
    m = F ÷ a
    m = 630000 ÷ 22 = 28636.36... kg
  4. Round to 2 significant figures
    m = 29000 kg

✅ Correct answer

Mass = 2.9 × 10⁴ kg or 29000 kg to 2 significant figures.

🧠 Exam technique

  • Convert Mach number to speed before calculating acceleration.
  • Make sure the answer is in m/s, not Mach units.
  • Use the correct physics equation: force = mass × acceleration
  • Give the final answer to 2 significant figures exactly as asked.

❌ Common errors

  • Using Mach numbers directly in the acceleration calculation without converting to m/s.
  • Forgetting to subtract the starting speed from the final speed.
  • Using a = v ÷ t instead of a = Δv ÷ t .
  • Rounding too early and losing accuracy.
  • Giving the final answer in the wrong number of significant figures.
How the 6 marks are awarded: 1 mark for working out the change in speed, 1 mark for the acceleration calculation, 1 mark for using m = F ÷ a , and marks for correct substitutions/calculations leading to the final answer. The final mark is only for a valid calculation using the correct equations.

Model answer to learn

Part (a) model response

At maximum power the forward force of the engines is constant. As the aeroplane accelerates, air resistance increases. The resultant force is force from engines minus air resistance, so the resultant force decreases. Since acceleration is directly proportional to resultant force, the acceleration decreases and is not constant.

Part (b) model response

Change in speed = (25.5 − 5.5) × 330 = 6600 m/s.
Acceleration = 6600 ÷ 300 = 22 m/s².
Mass = 630000 ÷ 22 = 28636.36... kg = 2.9 × 10⁴ kg to 2 significant figures.

Quick revision checklist

Remember

  • Acceleration is caused by resultant force.
  • More air resistance means smaller resultant force.
  • Mach numbers must be converted using Mach 1 = 330 m/s.

In the exam

  • Show each stage clearly.
  • Write units at every step.
  • Check the final rounding.

Topics

Physics · P5: Forces

Question and mark scheme from the AQA GCSE Combined Science: Trilogy examination, Physics Paper 2 (Higher), 2021. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.