Velocity, not displacement, is the convenient quantity for impulse analysis

Evidence

A sudden impulse to a body at rest has the effect of instantly imparting a velocity to the point receiving the blow. At first, displacement at the impact point is very small; displacement equals velocity × time, so displacement takes some time. … The energy imparted to the system by the hammer is the applied force times the velocity attained by the point of impact, summed over the course of the impulse. This is why velocity response is so convenient: a hammer tap produces the velocity instantaneously, and the velocity is the quantity we seek when determining power. — Eric J. Heller, Why You Hear What You Hear- An…, 1078

Categorization

• DEFINE: Clarifies why velocity response (instantaneous at impact) rather than displacement is the natural analytic quantity for impulses.