It sounds like this“If I'm going twice as fast, I need twice as far to stop.”
Thinking twice the speed needs twice the stopping distance
Why it feels right
Most distances scale directly with speed: at twice the speed you cover twice the ground in a minute, so it is natural to assume stopping works the same way. Many drivers carry a loose rule in their head that the gap should grow in step with speed.
Why it’s wrong
With the same braking force, the energy to remove is four times larger, so the distance is four times longer. At 30 km/h a car stops in about 5 m, and at 60 km/h in about 20 m, plus whatever distance you travel while reacting.
A worked example
The brakes can only remove energy as fast as they work over distance. A steady braking force F does work F x d, and that must equal the car's kinetic energy, half m v squared. So d = m v squared / 2F, and with the deceleration a = F / m, d = v squared / 2a.
For typical braking on a dry road, a is about 7 m per second squared. At 30 km/h (8.33 m/s) the braking distance is 69.4 / 14, about 5 m. At 60 km/h (16.67 m/s) it is 277.8 / 14, about 20 m. At 90 km/h (25 m/s) it is about 45 m, nine times as far as at 30.
The distance you travel while reacting is separate, and does grow in step with speed: at 1 second of reaction, 8 m at 30 km/h and 17 m at 60 km/h. So the total stopping distance grows between direct and squared, but the braking part, which is what the brakes have to do, grows with the square.
How to catch yourself
- You leave a gap that grows only in step with speed.
- You think 60 mph needs twice the stopping distance of 30.
- You are surprised how much worse a collision at 60 is than at 30.
What to hold instead
Braking removes energy at a steady rate over distance. Four times the energy needs four times the distance, so doubling speed quadruples the braking distance: about 5 m at 30 km/h and 20 m at 60 km/h.
Where you’ll meet it
- Judging a safe following distance.
- Reading about speed limits near schools.
- Understanding why speed matters in a crash.
Questions people ask
- Why does doubling speed quadruple the braking distance?
- Because the car's kinetic energy goes with the speed squared, and a steady braking force removes energy in proportion to distance. Four times the energy means four times the distance.
- What is the typical stopping distance at 30 mph?
- In the UK Highway Code, 23 metres in all, of which 9 m is thinking distance and 14 m is braking distance. At 60 mph it is 73 m, with 18 m thinking and 55 m braking.