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Difficulty: MediumSpeed Control and Following Distance

Doubling a vehicle's driving speed from 30 mph30\text{ mph} to 60 mph60\text{ mph} quadruples the braking distance required to bring the vehicle to a complete stop.

Answer: Answer

Answer

True. Doubling driving speed quadruples the braking distance because kinetic energy increases with the square of vehicle speed.
The statement is true because vehicle braking distance increases proportionally with the square of speed. Doubling speed quadruples the vehicle's kinetic energy, requiring four times the physical distance to stop.

Step-by-Step Solution

1
Analyze the mathematical relationship between speed and kinetic energy
Kinetic energy is calculated using Ek=12mv2E_k = \frac{1}{2}mv^2, where vv represents vehicle speed.
Work required by the brakes to stop a vehicle is directly proportional to its kinetic energy.
2
Calculate the factor change when speed is doubled
Replacing vv with 2v2v gives (2v)2=4v2(2v)^2 = 4v^2, showing a 4-fold increase in kinetic energy.
A four-fold increase in kinetic energy requires four times as much braking distance to stop.

Key Concept

Impact of Speed on Braking Distance
Estimated Time:45s
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Topics

Speed Control and Following Distance

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