Science Puzzle
How Much Further Does a Faster Car Need to Stop?
The UK Highway Code says a car travelling at 30 mph needs about 23 metres to stop. That's 9 metres travelled while the driver spots the danger and moves their foot to the brake, plus 14 metres while the brakes bring the car to a halt.
At 60 mph, the thinking distance doubles to 18 metres, because the car covers twice as much ground in the same reaction time. What happens to the 14 metres of braking distance?
The Answer
It quadruples. The Highway Code gives a braking distance of 55 metres at 60 mph, so the total stopping distance is 73 metres, more than three times the distance at 30 mph.
To stop, the brakes have to get rid of all the car's kinetic energy, its energy of movement, by turning it into heat. Kinetic energy depends on the square of the speed: double the speed and the car carries four times the energy. Brakes can only remove that energy at about the same rate for every metre travelled, so four times the energy takes about four times the distance.
Thinking distance only doubles, because it's simply the speed multiplied by the driver's reaction time. At 70 mph the total climbs to 96 metres, roughly the length of a football pitch, of which 75 metres is braking.
The square works the other way too, which is why lower speed limits near schools make such a difference. At 20 mph the Highway Code's total stopping distance is just 12 metres.
The principle: Kinetic energy rises with the square of speed. Doubling the speed of a car quadruples the energy its brakes must remove and so roughly quadruples its braking distance.