Which vector quantity equals the integral of force over time? Impulse is the vector quantity defined by that integral.
For a time-varying force, impulse is written J = ∫F dt over the relevant time interval. Because force has direction, impulse has direction too. Its SI unit is the newton-second, equivalent to the kilogram-metre per second used for momentum.
Impulse is especially useful for collisions and impacts, where a large force may act for only a short time. A golf club striking a ball, a bat hitting a baseball, or airbags slowing a passenger all involve impulse. The same impulse can result from a large force over a brief interval or a smaller force over a longer one.
A common mix-up is confusing impulse with force. Force describes an instantaneous push or pull, while impulse describes the accumulated effect of force over time. Newton's second law connects them: impulse equals the object's change in momentum.