The second car is drawn behind yours, braking from the same line.
Downhill is negative. Gravity is helping the car along instead of the tyres.
The Highway Code figures are not a measurement of your car. Work backwards from them and they assume a 0.67 second reaction and 0.67 g of braking — brisk reactions and, by modern standards, modest brakes. On a dry road a current car beats them comfortably. In the wet it does not.
| Speed | Official total | This car, here | Difference | Thinking | Braking |
|---|
No changes to this tool’s own behaviour since the earliest archived release (v3.70). The full history for the site is in the changelog.
Thinking distance is how far you travel before the brakes are touched: speed multiplied by your reaction time. It is linear in speed, and no amount of engineering shortens it. At 70 mph you cover 31 metres every second.
Braking distance is v² ÷ 2a, where the deceleration comes from the friction between four tyre contact patches and the road. It is quadratic, which is the origin of the rule everybody is taught.
Double your speed and your braking distance quadruples. That is exactly right, and it follows from kinetic energy going as the square of speed — twice as fast means four times the energy for the same brakes to turn into heat.
But the number on the sign is the total, and total distance does not quadruple, because thinking distance merely doubles. Going from 30 to 60 mph roughly trebles the total, not quadruples it. The rule is right about the physics and wrong about the answer, and almost nobody quoting it notices the difference.
Forget total distances for a moment. Ask instead how fast you are still going when you reach the point where a slower car would already have stopped.
At the Highway Code's own assumptions, a car doing 30 mph stops in 23 metres. A car doing 40 mph arrives at that same point still doing very nearly 30. It has not shed the extra ten miles an hour — it has not shed anything at all. It is still travelling at the speed limit when it gets to where the other car was already stationary.
You cannot fit better brakes to your attention. At 70 mph, the difference between an alert driver and one reading a message is 73 metres of road covered before the brakes are touched — more than two thirds of the entire official stopping distance, spent doing nothing.
A point mass, constant friction, and brakes that reach full effect instantly. Real stops have brake build-up, weight transfer onto the front tyres, ABS cycling, and fade. Friction coefficients vary enormously with tyre compound, tread depth, temperature and road age; the values here are mid-range figures and every distance should be read as a comparison rather than a promise. Reaction time is one number where reality is a distribution with a long tail — and the tail is where the collisions are. This is arithmetic, not advice, and it is no substitute for leaving a gap.