What is the general definition of impulse?

Impulse is defined as the change in momentum of an object when a force is applied over a time interval. The mathematical representation of impulse is given by the integral of force with respect to time, which is expressed as I = ∫ F dt. This formulation captures the cumulative effect of a force acting over the duration of time, allowing for varying forces to be accounted for.

The integral signifies that you sum the force applied at each instant, multiplied by the infinitesimal time intervals, to find the total impulse. This concept is critical in understanding the relationship between force and motion, particularly in scenarios where forces are not constant.

Additionally, while other expressions like I = ∆p (the change in momentum) are equivalent but do not specify how that change occurs over time, the integral formulation emphasizes the application of forces and their influence over time, which is fundamental in physics.