BRAKING
Braking distance grows as v² — double your speed, quadruple the road; the v² law, priced.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
The question
A car travels at speed v when the driver spots a hazard. How much road does it take to come to a full stop, counting both the driver and the brakes?
Two parts
First a reaction stretch at constant speed while the driver responds, then a braking stretch. During braking, all the kinetic energy ½mv² is turned into heat by the friction force.
Solve
Work-energy gives the braking distance directly: d_brake = v²/2a. Because it grows with the square of speed, a small increase in v costs a large increase in stopping distance.
The stop
Watch the kinetic-energy bar drain into the heat bar as the car decelerates. The car coasts through the reaction zone, then sheds speed until every joule has become friction heat.
The v² law
Double the speed and the braking distance quadruples — the amber ghost marks it. Reaction distance only doubles, because it is linear in v. Speed is far more dangerous than it feels.