# Impulse (physics)

In classical mechanics, impulse (symbolized by J or Imp) is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector quantity. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the resultant direction. The SI unit of impulse is the newton second (N⋅s), and the dimensionally equivalent unit of momentum is the kilogram meter per second (kg⋅m/s). The corresponding English engineering unit is the pound-second (lbf⋅s), and in the British Gravitational System, the unit is the slug-foot per second (slug⋅ft/s).

Impulse
Common symbols
J, Imp
SI unitnewton-second (Ns) (kgm/s in SI base units)
Other units
pounds
Conserved?yes
Dimension${\displaystyle {\mathsf {L}}{\mathsf {M}}{\mathsf {T}}^{-1}}$

A resultant force causes acceleration and a change in the velocity of the body for as long as it acts. A resultant force applied over a longer time, therefore, produces a bigger change in linear momentum than the same force applied briefly: the change in momentum is equal to the product of the average force and duration. Conversely, a small force applied for a long time produces the same change in momentum—the same impulse—as a larger force applied briefly.

${\displaystyle J=F_{\text{average}}(t_{2}-t_{1}).}$

The impulse is the integral of the resultant force (F) with respect to time:

${\displaystyle J=\int F\,\mathrm {d} t.}$