The key to understanding why braking distance quadruples when speed doubles lies in kinetic energy. KE = ½mv². When you brake, the braking force transfers ALL the kinetic energy away (converting it to thermal energy in the brakes and tyres).
Work done by brakes = braking force × braking distance = KE = ½mv²
If the braking force is constant (same brakes, same road conditions): braking distance = mv² / (2 × braking force). Since braking distance is proportional to v², doubling the speed quadruples the braking distance.
This is why modern cars have ABS (Anti-lock Braking Systems) — by preventing wheel lock-up, maximum friction is maintained throughout braking, minimising stopping distance.
This how it works covers Why Braking Distance Scales with v²: The Energy Connection within Stopping Distances for GCSE Physics. Revise Stopping Distances in Forces for GCSE Physics with 15 exam-style questions and 5 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 12 in this topic. Use this how it works to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Stopping Distances
What is the correct definition of stopping distance?
Explain why a car travelling at higher speed has a greater braking distance than a car travelling at lower speed, assuming the same braking force.