# Impulse-Momentum Calculator

## Calculator Use

The Impulse Momentum Calculator uses the formula FΔt = mΔv, or force F multiplied by the change in time Δt equals mass m times the change in velocity Δv.

Calculate force F, change in time Δt, mass m, velocity change Δv, initial velocity v_{1} or final velocity v_{2}. We also calculate impulse J (Δp) and provide it below the answer for all calculations.

## Impulse-Momentum Formula

Where:

- F = applied force
- Δt = change in time
- m = mass
- Δv = change in velocity

In this calculator we use Δt as the time interval. Instead of entering initial time t_{1} and final time t_{2}, just enter the elapsed time.

You may recognize the left side of the impulse-momentum equation from the impulse formula:

and the right side of the equation from the momentum formula:

Change in momentum can be written as:

As impulse is the change in momentum we get the impulse-momentum equation from the equality:

## Calculations Using the Impulse Momentum Formula:

Use the impulse momentum equation to find force, elapsed time, mass, change in velocity, v_{1}, or v_{2}.

Calculate F | Given m, Δv, Δt

Calculate force given mass, change in velocity and change in time.

Calculate F | Given m, v2, v1, Δt

Calculate force given mass, initial velocity, final velocity and change in time.

Calculate Δt | Given m, Δv, F

Calculate elapsed time given mass, change in velocity and force.

Calculate Δt | Given m, v2, v1, F

Calculate elapsed time given mass, initial velocity, final velocity and force.

Calculate m | Given F, Δt, Δv

Calculate mass given force, change in time and change in velocity.

Calculate m | Given F, Δt, v2, v1

Calculate mass given force, change in time, initial velocity and final velocity.

Calculate Δv | Given F, Δt, m

Calculate change in velocity given force, change in time and mass.

Calculate v1 | Given F, Δt, m, v2

Calculate initial velocity given force, change in time, mass and final velocity.

Calculate v2 | Given F, Δt, m, v1

Calculate final velocity given force, elapsed time, mass and initial velocity.