AQA GCSE Combined Science: Trilogy Physics Paper 2 (Higher), 2022: Question 3

8 marks · Standard Demand difficulty · Extended Answer

Calculate the train’s velocity from its momentum and explain, using momentum ideas, why its velocity decreases after colliding with a stationary carriage.

Practise this question

Question

An exam page shows Question 03 about a child playing with a toy train on a bridge. Part 03.1 states that the momentum of the train at the bottom of the bridge is 0.216 kg m/s and the mass of the train is 180 g, then asks the student to calculate the velocity of the train at the bottom of the bridge and to use the Physics Equations Sheet; the answer line is labelled velocity in m/s. Part 03.2 says the train collides with a stationary carriage on the track and asks the student to explain why the train’s velocity after the collision is less than it was before, using ideas about momentum. The page includes a photo of a child pushing a toy train down a small bridge, with several lined answer spaces and marks shown beside each part.
Question text

03 Figure 4 shows a child playing with a toy train.

The train is on a bridge.

Figure 4

When the child lets go of the train, the train rolls down the bridge.

03.1 The momentum of the train at the bottom of the bridge is 0.216 kg m/s

mass of the train = 180 g

Calculate the velocity of the train at the bottom of the bridge.

Use the Physics Equations Sheet.

[4 marks]

11 Velocity = m/s

03.2 The train collides with a stationary carriage on the track.

Explain why the velocity of the train after the collision is less than it was before the

collision.

*10* Use ideas about momentum in your answer.

[4 marks]

Mark scheme

Show the mark scheme The mark scheme shows that for Question 03.1 the mass should first be converted to 0.180 kg, then momentum equals mass times velocity is written as 0.216 = 0.180 × v, followed by rearranging to v = 0.216 / 0.180 and the final answer v = 1.2 m/s. It awards four marks across the steps and allows correct working even if the mass conversion is not done. For Question 03.2, the marking points are that total momentum is conserved in the collision, the carriage gains momentum, the train loses momentum, and because momentum equals mass times velocity, the train’s velocity decreases; four marks are available in total.

Question 3

AO /

Question Answers Extra information Mark

Spec. Ref.

03.1 m = 0.180 1 AO2

6.5.5.1

0.216 = 0.180 × v allow a correct substitution using 1

an incorrectly / not converted

value of m

0.216 allow a correct rearrangement 1

v =

0.180

using an incorrectly / not

converted value of m

v = 1.2 (m/s) allow a correct calculation using 1

an incorrectly / not converted

value of m

AO /

Spec. Ref.

03.2 (total) momentum is conserved allow (total) momentum before 1 AO1

in the collision collision = (total) momentum 6.5.5.1

after collision

during the collision the 1

momentum of carriage

increases

so the momentum of train 1

decreases

since momentum = mass × allow since mass (of train) is 1

velocity, velocity (of train) constant, velocity (of train)

decreases decreases

Total Question 3 8

How to answer it

Standard Demand

Momentum and collision of a toy train

What this question tests

This question tests how to use the momentum equation momentum = mass × velocity , including converting grams to kilograms, rearranging the equation correctly, and explaining a collision using conservation of momentum. It also checks whether you can link a decrease in momentum to a decrease in velocity when mass stays the same.

Part 03.1 • Calculate the velocity

Part (a): Finding the train's velocity at the bottom of the bridge

4 marks

✅ Correct answer

  • Mass of train = 0.180 kg
  • Use momentum = mass × velocity
  • 0.216 = 0.180 × v
  • v = 0.216 ÷ 0.180
  • Velocity = 1.2 m/s

💡 Key knowledge

  • Momentum equation: p = mv
  • Momentum is measured in kg m/s
  • Mass must be in kg , not grams
  • 180 g = 0.180 kg

📐 Calculation steps

  1. Write the equation:
    momentum = mass × velocity
  2. Convert the mass:
    180 g = 0.180 kg
  3. Substitute the values:
    0.216 = 0.180 × v
  4. Rearrange:
    v = 0.216 ÷ 0.180
  5. Calculate:
    v = 1.2 m/s

🧠 Exam technique

  • You can earn marks method-by-method, not just for the final answer.
  • Show the unit conversion clearly to secure the first mark.
  • Then show substitution and rearrangement on separate lines.
  • Always write the final unit: m/s .

❌ Common errors

  • Forgetting to convert 180 g into 0.180 kg .
  • Using the wrong rearrangement, for example doing 0.180 ÷ 0.216 .
  • Missing the unit in the final answer.
  • Writing too many digits when the question only needs a sensible answer: 1.2 m/s is correct.
How the 4 marks are awarded:
1 mark for converting the mass to 0.180 kg
1 mark for correct substitution: 0.216 = 0.180 × v
1 mark for correct rearrangement: v = 0.216 / 0.180
1 mark for the correct answer: 1.2 m/s
Part 03.2 • Explain the collision

Part (b): Why the train's velocity decreases after the collision

4 marks

✅ Correct answer

A full-mark answer could be:

Total momentum is conserved in the collision. The carriage is stationary before the collision, so during the collision the momentum of the carriage increases. Therefore the momentum of the train decreases. Since momentum = mass × velocity and the mass of the train stays the same, the velocity of the train must decrease.

💡 Key knowledge

  • In a closed system, total momentum before = total momentum after.
  • A stationary object starts with zero momentum.
  • If one object gains momentum in a collision, another object must lose momentum.
  • If mass is constant, a decrease in momentum means a decrease in velocity.

🧠 Exam technique

  • This is a sequence question: link each idea in order.
  • Use the word total momentum, not just momentum on its own.
  • Mention both objects: the train and the carriage.
  • Finish by linking back to velocity using momentum = mass × velocity .

❌ Common errors

  • Saying momentum is “lost” instead of saying total momentum is conserved.
  • Talking only about energy instead of momentum. The question specifically asks for momentum ideas.
  • Not mentioning that the carriage gains momentum.
  • Saying the train slows down without explaining why in terms of momentum and constant mass.

📐 Structure your explanation step-by-step

  1. State the principle: total momentum is conserved .
  2. Say what happens to the carriage: its momentum increases .
  3. Then link to the train: the train's momentum decreases .
  4. Use the equation: momentum = mass × velocity .
  5. Because the train's mass is constant, its velocity decreases .
How the 4 marks are awarded:
1 mark for stating that total momentum is conserved in the collision
1 mark for stating that the carriage gains/increases momentum
1 mark for stating that the train therefore loses/decreases momentum
1 mark for linking this to momentum = mass × velocity so the train's velocity decreases because its mass stays constant

Examiner insight: what separated full-mark answers?

🧠 What strong answers did well

  • They showed every line of working in part (a), especially the mass conversion.
  • They used the momentum equation correctly and rearranged it clearly.
  • In part (b), they gave a logical chain rather than one short vague sentence.
  • They referred to conservation of total momentum, not just “the train slows down”.

❌ Where students lost marks

  • Missing the grams-to-kilograms conversion.
  • Getting the correct method but not writing it clearly enough to gain all method marks.
  • Giving collision explanations about force or energy only.
  • Failing to explain that the carriage gains momentum, so the train's momentum must decrease.

Quick full-mark model answers

✅ Part 03.1 model answer

Mass = 180 g = 0.180 kg

Momentum = mass × velocity

0.216 = 0.180 × v

v = 0.216 ÷ 0.180 = 1.2 m/s

✅ Part 03.2 model answer

Total momentum is conserved in the collision. The carriage is stationary at first, so during the collision it gains momentum. Therefore the train's momentum decreases. Since momentum = mass × velocity and the train's mass stays the same, its velocity decreases.

Topics

Physics · P5: Forces

Question and mark scheme from the AQA GCSE Combined Science: Trilogy examination, Physics Paper 2 (Higher), 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.