# Impulse

In classical mechanics, an impulse changes the momentum of an object, and has the same units and dimensions as momentum. The SI unit of impulse is the same as for momentum, and is kilogram metres per second (kg m /s ). An impulse is calculated as the integral of force with respect to time.

[itex]\mathbf{I} = \int \mathbf{F}\, dt [itex]

where

I is the impulse, measured in kilogram metres per second
F is the force, measured in newtons
t is the time duration, measured in seconds

In the presence of a constant force, impulse is often written using the formula

[itex]\mathbf{I} = \mathbf{F}\Delta \mathbf{t} [itex]

where

[itex]\Delta t[itex] is the time interval over which the force (F) is applied.

Using the definition of force yields:

[itex]\mathbf{I} = \int \frac{d\mathbf{p}}{dt}\, dt [itex]
[itex]\mathbf{I} = \int d\mathbf{p} [itex]
[itex]\mathbf{I} = \Delta \mathbf{p} [itex]

It is therefore common to define impulse as a change in momentum.

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