Final answer:
When a car doubles its speed, its braking distance increases by a factor of four, due to the kinetic energy of the car being proportional to the square of its speed. This increase in braking distance is crucial for driving safety and maintaining safe following distances.
Step-by-step explanation:
When a car's speed doubles, the braking distance increases by a factor of four, assuming that all other factors like road conditions and vehicle response time remain constant. This relationship holds because the stopping distance is directly proportional to the square of the car's speed. The physical principle behind this is rooted in the equations of motion, particularly kinetic energy which scales with the square of velocity, and it is this energy that must be dissipated by the brakes to stop the vehicle.
For example, if a car traveling at 50 mph requires a certain distance to stop, doubling the speed to 100 mph will require four times the distance to stop under the same conditions. This is critical information for ensuring safe following distances and understanding the risk of higher speeds. The increased distance needed at higher speeds is due to the energy that must be dissipated, and the fact that the energy quadruples when speed doubles.
An important real-world application of this principle is for driving safety. In reduced speed zones, such as near schools, the lower speed limit significantly reduces the potential stopping distance required, helping to prevent accidents in areas where children or other pedestrians are present.