Impulse

In physics, impulse is the change in an object's momentum resulting from a force acting over a period of time. It is defined as the integral of force with respect to time over the interaction interval: J = ∫ F dt. By the impulse–momentum theorem, impulse equals the change in momentum, J = Δp = p_f − p_i. The concept links the force applied to how much the object's motion changes.

Units for impulse are newton-seconds (N·s) or kilogram-meters per second (kg·m/s). A large impulse can result from a large force acting briefly or a smaller force acting for a longer time; different force–time profiles can yield the same impulse.

In electronics and signal processing, an impulse refers to a very short, ideally instantaneous event. The Dirac delta function δ(t) represents a unit impulse. The impulse response h(t) of a linear time-invariant system describes its output to an impulse input, and system outputs can be analyzed by convolving the input with h(t).

In everyday language, impulse also denotes a sudden urge to act. Impulse control refers to the ability to resist such urges or delay gratification. The term thus spans concepts in physics, engineering, and psychology, with each field using a related but distinct meaning.