What theorem says impulse equals the change in momentum?

What theorem says impulse equals the change in momentum? The impulse–momentum theorem states that impulse equals the change in momentum.

In symbols, J = Δp, or, for a varying net force, ∫F dt = p₂ − p₁. The result follows directly by integrating Newton's second law, which expresses force as the rate of change of momentum. It applies whether the force is steady or changes throughout the interaction.

The theorem makes short-duration events easier to analyze. In a collision, the force may vary too rapidly to measure conveniently at every instant, but its total impulse can still be found from the object's change in momentum. A padded catcher’s mitt increases stopping time, reducing average force for the same momentum change.

The theorem is often confused with the work–energy theorem. Impulse changes momentum, whereas work changes kinetic energy. Momentum and impulse are vectors, so direction matters; kinetic energy and work are scalar quantities.