Braking distance scales with the square of speed — 20% faster needs 44% more room, and twice the speed needs four times.
v² = u² + 2as with v = 0 gives s = u²/(2a). The speed is squared and the deceleration is not, so distance grows far faster than the speedometer suggests. At a steady 10 m/s², 30 m/s takes 45 m and 60 m/s takes 180 m.
This is the braking phase only. Real stopping distance adds thinking distance, which grows linearly with speed and can be a third of the total at low speeds. Deceleration is also not constant — it falls off as tyres unload and on a wet or loose surface may be half of what you assumed. Treat it as the floor, never the number.
At 50 km/h the rule says 12.294 m and the exact answer is 33.127 m — 63% low. It is never within 10% anywhere in this range.
Braking distance really does go as the square. Stopping distance does not, because before any of it happens you have to notice — and that part is LINEAR in speed. At 20 km/h more than half the tarmac you use is spent still deciding. The square only takes over on the motorway, which is the one place people already expect it.
The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.
Estimate with the rule, then check it against the calculator that models it properly.
Open SUVAT Calculator →Braking distance scales with the square of speed — 20% faster needs 44% more room, and twice the speed needs four times. v² = u² + 2as with v = 0 gives s = u²/(2a).