Final answer:
Doubling the speed of a vehicle quadruples the stopping distance because stopping distance is proportional to the square of the speed, assuming constant deceleration. This demonstrates why reduced speed zones are crucial for safety in areas like school zones.
Step-by-step explanation:
The question addresses stopping distances at different speeds within the field of Physics. When considering the scenario where a vehicle doubles its speed, the stopping distance does not simply double; it increases by a factor greater than two.
This is because stopping distance is proportional to the square of the speed when deceleration is constant. That is, doubling the speed quadruples the stopping distance, under the assumption that the deceleration remains the same.
Thus, if you double your speed, the formula for kinetic energy (which is proportional to the square of the speed) indicates that it will take much more distance to stop than at the original speed.
This concept is essential for understanding why areas such as school zones have reduced speed limits - to ensure that cars can stop in a shorter distance, thus increasing safety for pedestrians.