In classical mechanics, an 'impulse' is defined as the integral of a force with respect to time:mathbf = int mathbf, dt whereI is impulse (sometimes marked J),F is the force, anddt is an infinitesimal amount of time.A simple derivation using Newton's second law yields:mathbf = int frac}, dt mathbf = int dmathbf mathbf = Delta mathbf As a result, an impulse may also be regarded as the change in momentum of an object to which a force is applied. The impulse may be expressed in a simpler form when