Calculate the momentum of a 1500\,kg car travelling at 20\,m/s. [2 marks]

OCR OCR 2019-style practice: A trolley of mass 2.0\,kg moves at 3.0\,m/s and collides with a stationary trolley of mass 1.0\,kg. They stick together. Calculate their common velocity after the collision, using conservation of momentum.

A P2 Higher Calculate question on conservation of momentum. Total momentum before = total momentum after (1 mark). Before: p = mv = 2.0 × 3.0 + 1.0 × 0 = 6.0\,kg m/s. After, the combined mass is 2.0 + 1.0 = 3.0\,kg moving at velocity v, so 3.0 × v = 6.0 (1 mark). Solving gives v = 6.03.0 = 2.0\,m/s (1 mark). Markers reward the conservation statement, the total momentum before, and the correct final velocity. A common error is to forget the stationary trolley still contributes to the total mass after the collision.

EnglandPhysicsSyllabus dot point

What is momentum, why is it conserved in collisions, and how does it explain road-safety features?

Momentum as mass times velocity, the conservation of momentum in collisions and explosions, force as the rate of change of momentum, and how safety features increase collision time to reduce force.

A focused answer to OCR Gateway GCSE Physics A topic P2 on momentum, covering momentum as mass times velocity, the conservation of momentum in collisions and explosions, force as the rate of change of momentum at Higher tier, and how safety features reduce the force in a crash.

Generated by Claude Opus 4.89 min answerUpdated 2026-06-02

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What this topic is asking
Momentum
Conservation of momentum
Force and the rate of change of momentum (Higher)
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What this topic is asking

OCR wants you to calculate momentum, apply conservation of momentum to collisions and explosions, and (at Higher tier) explain force as the rate of change of momentum and how safety features reduce the force in a crash. This is part of topic P2.2 of the OCR Gateway Physics A (J249) specification.

Momentum

A heavy object moving fast has a large momentum and is hard to stop; a light object or a slow one has a small momentum. Because momentum is a vector, objects moving in opposite directions have momenta of opposite sign, which matters when you add them up in a collision.

Conservation of momentum

So when two objects collide and stick together, the total momentum is shared by the combined mass. In an explosion that starts from rest, the total momentum stays zero, so the fragments move off in opposite directions with equal and opposite momenta (this is why a gun recoils backwards as the bullet goes forwards). Remember to treat momenta in opposite directions as having opposite signs.

Force and the rate of change of momentum (Higher)

This is the physics behind road-safety features. In a crash, the occupant's momentum must be reduced to zero. Crumple zones, airbags and seatbelts all act to increase the time over which this change happens, so the force on the occupant is reduced, lowering the risk of injury. A safety helmet and crash mats work the same way.

Conservation of momentum in a collision

A railway truck of mass $4000\,\text{kg}$ moving at $2.0\,\text{m/s}$ collides with a stationary truck of mass $2000\,\text{kg}$ . They couple together. Calculate their common velocity after the collision.

step 1: State conservation of momentum

In a closed system the total momentum before equals the total momentum after.

step 2: Find the total momentum before

Only the first truck is moving: $p = mv = 4000 \times 2.0 + 2000 \times 0 = 8000\,\text{kg m/s}$ .

step 3: Write the momentum after

After coupling, the combined mass is $4000 + 2000 = 6000\,\text{kg}$ moving at velocity $v$ : total momentum $= 6000 \times v$ .

step 4: Set equal and solve

$6000 \times v = 8000$ , so $v = \dfrac{8000}{6000} = 1.3\,\text{m/s}$ (to two significant figures). The coupled trucks move off at about $1.3\,\text{m/s}$ in the original direction.

Try this

Q1. Calculate the momentum of a $1500\,\text{kg}$ car travelling at $20\,\text{m/s}$ . [2 marks]

Cue. $p = mv = 1500 \times 20 = 30\,000\,\text{kg m/s}$ .

Q2. Explain why a seatbelt that stretches a little in a crash reduces the force on the wearer. [2 marks]

Cue. It increases the time over which the wearer's momentum falls to zero, so for the same change of momentum the force is smaller.

Exam-style practice questions

Practice questions written in the style of OCR exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

OCR 20193 marksA trolley of mass

2.0\,\text{kg}

moves at

3.0\,\text{m/s}

and collides with a stationary trolley of mass

1.0\,\text{kg}

. They stick together. Calculate their common velocity after the collision, using conservation of momentum.

Show worked answer →

A P2 Higher Calculate question on conservation of momentum. Total momentum before $=$ total momentum after (1 mark). Before: $p = mv = 2.0 \times 3.0 + 1.0 \times 0 = 6.0\,\text{kg m/s}$ . After, the combined mass is $2.0 + 1.0 = 3.0\,\text{kg}$ moving at velocity $v$ , so $3.0 \times v = 6.0$ (1 mark). Solving gives $v = \dfrac{6.0}{3.0} = 2.0\,\text{m/s}$ (1 mark). Markers reward the conservation statement, the total momentum before, and the correct final velocity. A common error is to forget the stationary trolley still contributes to the total mass after the collision.

OCR 20224 marksExplain, in terms of momentum and force, why a car's crumple zone and a passenger's airbag reduce the risk of injury in a collision.

Show worked answer →

A P2 Explain question worth four marks linking momentum to safety. In a crash the occupant's momentum must be reduced to zero, which requires a force to act over a time (1 mark). A crumple zone and an airbag increase the time taken for the momentum to change (the occupant slows over a longer time) (1 mark). Because force equals the rate of change of momentum, increasing the time for the same change in momentum reduces the force on the occupant (1 mark). A smaller force means less chance of injury (1 mark). Markers reward the same change of momentum, increased collision time, force as rate of change of momentum, and the reduced force.

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Sources & how we know this

OCR GCSE (9-1) Physics A (Gateway Science) J249 specification — OCR (2016)