Free · Dynamics calculators — Why things move ➡️

Signed Impulse, Momentum Change & Average Force

Connect initial and final velocity, momentum change, signed impulse and average net force over a positive time interval.

Formula & worked example
Private in your browser
No signup

Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 2 kg object changing from 3 to −1 m/s has an impulse of −8 N·s. Over 0.5 seconds, its average net force is −16 N.

Impulse = m(final velocity − initial velocity) = final momentum − initial momentum = average force × time

Worked example

Enter these known values and leave the other values blank.

Mass (m): 2 kg
Initial velocity (v₁): 3 m/s
Final velocity (v₂): -1 m/s
Time interval: .5 sec

Velocity change (Δv): -4 m/s
Average net force over the interval: -16 N
Impulse (J): -8 N⋅s
Initial momentum (p₁): 6 N⋅s
Final momentum (p₂): -2 N⋅s

Assumptions and limitations

All velocities, momenta, impulse and force are signed components along one chosen axis. Choose a positive direction and use it consistently.
Mass is positive and constant. The momentum relation is classical and does not include relativistic effects or variable-mass systems.
Force is the average net force over the entered interval. Multiplying that average by time gives net impulse; it does not reveal peak force.
The interval must be positive. Equal initial and final velocities give zero momentum change, zero net impulse and zero average net force.
A zero impulse cannot uniquely determine mass from velocity change when that change is also zero. Enter enough independent data for the desired unknown.

Common questions

Does a negative impulse mean the result is invalid?

No. It means the momentum change points opposite to the chosen positive direction.

References

Bookify accepts zero velocity change, net impulse and average force for unchanged momentum. Bookify uses the exact pound-force second of 4.4482216152605 newton seconds for impulse and momentum. One kip is exactly one thousand pound-force, using the international pound and standard gravity. The pound-force uses the exact international pound and standard gravity instead of the rounded captured factor.

Explore dynamics calculators — why things move ➡️ or browse all physics calculators.