Momentum and impulse

Linear momentum is defined as p = mv. It is a vector quantity pointing in the direction of velocity, measured in kg·m/s, and it captures how hard it is to stop a moving object — a heavy truck at low speed and a light car at high speed can carry the same momentum.

Impulse is J = FΔt, the effect of a force applied over an interval of time. The impulse-momentum theorem states that J = Δp, so FΔt = mΔv. This is a restatement of Newton's second law: net force equals the rate of change of momentum. The practical consequence is that extending the time over which a collision occurs reduces the force required to produce the same momentum change. A car airbag, a crumple zone, and bending your knees on landing all work this way — the change in momentum is fixed, so lengthening Δt lowers the peak force. Graphically, impulse is the area under a force-versus-time curve, which lets you handle forces that vary during a collision.

When no external force acts on a system, total momentum is conserved, and this is what makes collision problems solvable. In an elastic collision both momentum and kinetic energy are conserved; in an inelastic collision only momentum is conserved, with the rest of the kinetic energy converted to heat, sound, and deformation. In a perfectly inelastic collision the objects move off together with a common velocity. Conservation applies independently along each coordinate axis, so two-dimensional collisions split into separate x and y equations.

AP Physics 1 devotes a full unit to systems, momentum, and impulse. Expect questions that read impulse off a force-time graph, apply conservation of momentum to collisions and explosions, and explain qualitatively why increasing collision time reduces force — a favorite free-response prompt.