How does stopping distance change when speed doubles?

Stopping distance increases with the square of speed, not linearly. Doubling speed roughly quadruples the distance needed to stop. This is because braking energy is proportional to the square of speed, so twice as fast means four times as much kinetic energy that the brakes must dissipate. Total stopping distance has three components: perception distance (how far you travel while recognizing the hazard), reaction distance (how far you travel while moving your foot to the brake), and braking distance. Perception and reaction distances scale linearly with speed; braking distance scales with the square. The implication: small speed reductions produce disproportionately large safety gains, and high-speed crashes are far more violent than the speed difference alone suggests.