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Impulse-Momentum Calculator

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Enter any two of force, time, and impulse - the third is calculated automatically. Impulse equals the resulting change in momentum.

Impulse-Momentum Calculator

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Impulse =
10 N·s
Impulse (N·s) and momentum (kg·m/s) are numerically and dimensionally equivalent units.

The formula

Impulse = Force x Time = Change in momentum
Example

A 50N force applied for 0.2 seconds: impulse = 50 x 0.2 = 10 N·s - meaning the object's momentum changed by exactly 10 kg·m/s.

Step-by-step guide

  1. Fill in any two values - force, time, or impulse - and leave the third blank.
  2. Read the calculated result, which equals the resulting change in momentum.

Why airbags and padding actually work

Impulse equals force multiplied by time, and for a given change in momentum (say, a person's body stopping in a crash), that impulse is fixed - but how it's delivered isn't. Stretching the same impulse over a longer time (via an airbag or padding that extends the stopping time) means less peak force is needed at any given instant, which is exactly why airbags, crumple zones, and padded landing mats reduce injury: they don't change the total impulse, just spread it out to lower the force.

Common mistakes

Assuming impulse and force are the same thing - impulse specifically accounts for how long a force is applied, not just its magnitude.
Forgetting that a constant-force assumption is a simplification - real-world forces during impacts often vary rapidly over very short times, and this formula gives the effective average force.

Frequently asked questions

Why are impulse and momentum measured in equivalent units?

Because impulse is literally defined as the change in momentum - the impulse-momentum theorem states they're the same physical quantity viewed from two different but equivalent formulas (Force x Time, or Mass x change in velocity).

How does this relate to Newton's second law?

Newton's second law (F=ma) and the impulse-momentum relationship are two ways of describing the same underlying physics - impulse-momentum is especially useful when force varies over time or acts only briefly, like during an impact.

Why do longer collision times reduce injury?

Because for a fixed impulse (the total momentum change), a longer time means a lower average force is needed - this is the entire physics principle behind airbags, helmets, and padded surfaces.

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