Final answer:
The impact and braking distance is four times greater when a car's speed doubles from 20 mph to 40 mph because kinetic energy is proportional to the square of the velocity.
Step-by-step explanation:
When the speed doubles from 20 mph to 40 mph, the impact and braking distance is four times greater. This is because the kinetic energy of a moving vehicle is directly proportional to the square of its velocity, as indicated in physics equations related to motion. Specifically, if you increase the speed of a car, the kinetic energy of the car increases by the square of the factor by which the speed increases. So, doubling the speed (a factor of 2) results in an increase of the kinetic energy by a factor of 22, which is 4. Consequently, both the energy that needs to be dissipated during braking and the potential impact energy increase by this factor.