Conceptly
LessonsFormulasPricing
Sign inStart free
Conceptly
TermsPrivacyRefunds
© 2026 · Physics for everyone
  1. Home
  2. Lessons
  3. Mechanics
  4. Momentum and Impulse
All lessons Mechanics20 min

Momentum and Impulse

Complete each stage to unlock the next one.

← Power and EfficiencyCollisions and Conservation of Momentum →
01
Hook
02
Explore
03
Formalize
04
Practice
05
Challenge
Interactive simulation
01

Hook

A 0.145 kg baseball flies past at 40 m/s; a 45 kg child jogs by at 3 m/s. The ball moves 13× faster — so it must be harder to stop. Which one would actually flatten you?

02

Explore

Complete previous stage
03

Formalize

Complete previous stage
04

Practice

Complete previous stage
05

Challenge

Complete previous stage
Spoilers

Momentum and Impulse — summary and key formula

ShowHide

The question

A 0.145 kg baseball flies past at 40 m/s; a 45 kg child jogs by at 3 m/s. The ball moves 13× faster — so it must be harder to stop. Which one would actually flatten you?

Speed alone is a trap: what makes something hard to stop is mass and speed together — momentum, p = mv. The ball carries 5.8 kg·m/s; the child carries 135 — about 23× more. To change that momentum you need a force acting over time, and that single idea explains airbags, crumple zones, and bending your knees on landing.

The key idea

Momentum p = mv measures 'quantity of motion' — why a slow lorry is harder to stop than a fast bicycle. To change momentum you apply a force over time, and that product is the impulse J=F⋅ΔtJ = F\cdot \Delta tJ=F⋅Δt. The impulse–momentum theorem says impulse equals the change in momentum: J=ΔpJ = \Delta pJ=Δp. Rearranged as F=Δp/ΔtF = \Delta p/\Delta tF=Δp/Δt, it tells you that stretching the contact time shrinks the force.

Impulse equals momentum change because Newton's second law, F = ma = m(Δv/Δt), times Δt gives F⋅Δt=mΔvF\cdot \Delta t = m\Delta vF⋅Δt=mΔv. Same law, accumulated over time. This is why airbags, crumple zones, and bending your knees all work: Δp is fixed, so stretching Δt shrinks the peak force F by the same factor. A cyclist hitting a wall (Δp=780 kg⋅m/s)(\Delta p = 780\,\text{kg}\cdot \text{m/s})(Δp=780kg⋅m/s) in 0.003 s feels 260 000 N — fatal; the same Δp over 3 s of cushioned stopping is 260 N — survivable. Same momentum change, 1000× less force. Crumple zones don't make the crash gentler by absorbing 'extra' impulse — they simply buy time.

The formula

p=mvJ=F Δt=ΔpF=ΔpΔtp = mv \qquad J = F\,\Delta t = \Delta p \qquad F = \frac{\Delta p}{\Delta t}p=mvJ=FΔt=ΔpF=ΔtΔp​
  • ·p = momentum (kg·m/s)
  • ·m = mass (kg)
  • ·v = velocity (m/s
  • ·a vector — direction matters)
  • ·J = impulse (N·s
  • ·same units as momentum: kg·m/s)
  • ·F = average force (N)
  • ·Δt = duration the force acts (s)
  • ·Δp = change in momentum = mΔv. Because Δp is usually fixed by the situation
  • ·the same momentum change can be delivered as a huge force over a tiny time or a gentle force over a long time.

Common mistake

Judging a collision by the peak force alone — what changes momentum is impulse = force × time, so a small force over a long time can match a big force over a short time.

What to remember

  • ·Momentum p = mv is a vector — direction matters.
  • ·Impulse = force × time = change in momentum.
  • ·Spreading a collision over more time (airbags) lowers the peak force.