*Question*:How is the braking distance of a car related to the speed of a car?

The brakes must reduce the cars Kinetic energy to zero.

The brakes do this by doing work.

The work done by the brakes = the braking force x the distance travelled.

The amount of work that must be done by the brakes is proportional to the square of the cars speed.

The braking force itself and the mass are constant for a given car.

So the braking distance is also proportional to the square of the cars speed.

KE of car = WD by brakes

0.5 x mass of car x speed of car squared = braking force x braking distance.