Braking distance goes as the square of speed. Twice as fast is four times the distance under braking, because it is four times the kinetic energy for the same tyres to turn into heat.
Kinetic energy is a half m v squared, and friction removes it at a roughly constant rate per metre travelled. So the metres needed scale with v squared. It is why the gap that felt ample at 30 is nothing like enough at 60.
It is right about BRAKING distance and wrong about the number on the sign. Total stopping distance also contains thinking distance, which is speed times reaction time and therefore merely doubles — so going from 30 to 60 mph roughly trebles the total rather than quadrupling it. And the official figures assume 0.67 g of braking, which a modern car beats in the dry and misses badly in the wet.
Estimate with the rule, then check it against the calculator that models it properly.
Open Stopping Distance Calculator →