Impulse is a physical quantity representing the accumulated effect of a force acting over a time interval and is equal to the resulting change in momentum. For a constant force, impulse is the product of force and interaction time, while for a varying force it is obtained by integrating force with respect to time. Impulse is a vector because force and momentum change are vectors. The impulse-momentum theorem therefore provides a direct relationship between an interaction's force-time history and the resulting change in an object's motion. It is especially useful for short-duration events such as impacts, collisions, explosions and rapid mechanical interactions.
The relationship between Impulse and momentum follows from Newton's Second Law in its momentum form, which states that net external force equals the rate of change of momentum. Integrating this relationship over time gives the net impulse as the change in momentum. This formulation is more general than simply using force multiplied by time because real forces are often not constant. A force-time graph therefore contains direct information about impulse: the signed area under the net force-time curve represents the change in momentum. This makes impulse particularly valuable when the instantaneous force varies substantially during an interaction.
In collision analysis, Impulse explains why changing the duration of an impact can alter the force experienced by an object without changing the required overall momentum change. If the same change in momentum occurs over a longer time interval, the average force is reduced. Vehicle safety systems exploit this principle by managing how quickly occupants' momentum changes. Airbags and deformable structures can extend the duration over which the occupant's velocity changes, while helmets and protective padding can alter the force-time profile of impacts. The underlying conservation and momentum relationships remain unchanged, but the distribution of force over time changes the mechanical loading experienced by the object.
Impulse must be distinguished from force. Force describes an interaction at a particular instant or over a specified interval, whereas impulse incorporates both force magnitude and duration. A brief high-force event and a longer lower-force event can produce equal impulses if their integrated force histories are equal. They may nevertheless produce different peak forces, deformation patterns, vibrations and biological effects. Consequently, impulse alone does not provide a complete description of an impact; the detailed force-time profile can matter substantially when assessing structural response or injury risk.
Impulse is also useful in systems involving variable forces such as bouncing objects, spring impacts and fluid interactions. During a bounce, the object's momentum reverses or changes direction, so the impulse must account for the full vector change rather than merely comparing force magnitudes. When a ball strikes a rigid surface, the normal force generally varies rapidly during compression and restitution. Integrating that force over the contact interval yields the momentum change. Experimental force sensors can therefore be used to determine impulse directly from measured force-time data.
In one-dimensional problems, sign conventions are essential. If an object initially travels in the positive direction and subsequently reverses direction, the final velocity is negative under the chosen convention, so the momentum change can be substantially larger in magnitude than the initial momentum alone. Treating velocity as a positive speed can therefore lead to an incorrect impulse calculation. In multiple dimensions, the same principle applies through vector subtraction, with impulse components corresponding to changes in momentum components.
Impulse has applications beyond collisions. In propulsion, a thrust force acting over time transfers momentum to a vehicle. In sports, a racket, bat or foot applies force over a finite contact period, changing the momentum of an object. In mechanical engineering, impulse loads are considered when analysing hammers, presses, impact tools and machinery subjected to sudden loads. In fluid mechanics, momentum flux and pressure forces can be related through control-volume formulations, although the term impulse must be used carefully because fluid momentum transfer and rigid-body impact are not identical physical situations.
A common misconception is that increasing force always increases impulse regardless of duration. Impulse depends on the integral of force over time, so both magnitude and duration matter. Another misconception is that reducing force necessarily reduces momentum change; if the duration is increased appropriately, the same impulse can result. It is also important to distinguish net impulse from the impulse associated with one particular force. When several forces act during an interval, the total change in momentum is determined by the vector sum of all relevant impulses, including external forces such as gravity when their contribution is not negligible.
