Learn0625Papers 2, 4 · ExtendedMotion, forces and energyMomentum and impulse

Motion, forces and energy · Subtopic 7 of 10

Momentum and Impulse

Momentum is mass times velocity, $p=mv$ , and it has a direction. In any collision or explosion with no external force, the total momentum before equals the total after. A force changes momentum: $F=\dfrac{\Delta p}{\Delta t}$ , so spreading a change over a longer time means a smaller force.

Cambridge 5054 Paper 1Cambridge 5054 Paper 2Cambridge 0625 Papers 2, 4Cambridge 0625 Papers 1, 3Edexcel 4PH1 Paper 1PEdexcel 4PH1 Paper 2P≈ 30 minRevision 6 · updated 2026-10-27

Section 1 of 14

Learning objectives

Calculate momentum, remembering it's a vector.
Use conservation of momentum for collisions and explosions.
Calculate impulse and use $F=\dfrac{\Delta p}{\Delta t}$ .
Explain how crumple zones, airbags and helmets reduce forces.

Pause and think

Why does a fielder pull their hands back when catching a fast cricket ball?

Section 2 of 14

Core idea

Start hereWhy airbags save lives

In a crash, a passenger must lose all their momentum. Hit a dashboard and it happens in a few hundredths of a second; hit an airbag and it takes ten times longer. Same change, much gentler force.

The big idea

$p=mv$ ; total momentum is conserved in collisions. $F=\frac{\Delta p}{\Delta t}$ : a longer stopping time means a smaller force.

1. Conservation

A collision: trolleys stick together

Before:

2\times6=12

kg m/s. After:

3v=12

, so

v=4

m/s.

Why momentum is conserved

$F_{AB}=-F_{BA}$
Newton's third law: equal and opposite forces.
$F_{AB}\Delta t=-F_{BA}\Delta t$
Same contact time.
$\Delta p_A=-\Delta p_B$
Momentum gained by one is lost by the other.

Worked exampleTrolleys stick together

2 kg at 3 m/s hits 1 kg at rest; they join.

Goal: Final speed.
Strategy: Momentum before = after.

$2\times3+1\times0=6$
Before.
$3v=6\Rightarrow v=2\text{ m/s}$
Combined mass 3 kg.

Answer

2

m/s.

✓ CheckSlower than before, since more mass shares the momentum ✓.

2. Impulse and safety

Same change in momentum, different stopping times

Both areas (

F\times t=120

N s) are the same impulse. Spreading it over a longer time makes the force much smaller: that is how airbags, crumple zones and helmets protect you.

F\Delta t=\Delta p=mv-mu

$F\Delta t$: impulse (N s).

Worked exampleA passenger stopping

70 kg from 15 m/s: hard stop 0.05 s vs airbag 0.5 s.

Goal: Forces.
Strategy: $F=\Delta p/\Delta t$ .

$\Delta p=70\times15=1050$
All momentum lost.
$1050\div0.05=21000\text{ N}$
Hard stop.
$1050\div0.5=2100\text{ N}$
Airbag.

Answer

21\,000

N vs

2100

✓ CheckTen times the time, one tenth the force ✓.

Common misconceptionDirection Momentum is a vector: opposite directions need opposite signs.

Pause and think

Why does a gun recoil?

Summary

$p=mv$ ; conserved.
$F=\Delta p/\Delta t$ .

Impulse: Force × time = change in momentum.

HistoryDescartes and "quantity of motion". In

1644

René Descartes proposed that the total "quantity of motion" in the universe never changes. He got the details wrong (he ignored direction), but Huygens and Newton fixed it: the conserved quantity is mass times velocity, as a vector.

Fun factRockets push on nothing. Rockets work in space even though there's no air to push against. Hot gas shoots out backwards with momentum, so the rocket gains equal momentum forwards. It's the same reason a skateboarder rolls backwards when throwing a heavy ball forwards.

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