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Difficulty: HardSpeed Control and Following Distance

According to vehicle physical dynamics and speed control principles, doubling a vehicle's speed from 30 mph30\text{ mph} to 60 mph60\text{ mph} results in a doubling of the braking distance required to bring the vehicle to a complete stop on a dry, level surface.

Answer: Answer

Answer

The statement is False. Doubling speed increases required braking distance by four times due to kinetic energy quadrupling.
The statement is false because doubling a vehicle's speed quadruples (22=42^2 = 4) the required braking distance, as braking distance scales directly with kinetic energy (Ek=12mv2E_k = \frac{1}{2}mv^2).

Step-by-Step Solution

1
Analyze the relationship between vehicle speed and kinetic energy
Kinetic energy is calculated as Ek=12mv2E_k = \frac{1}{2}mv^2, meaning energy increases with the square of velocity.
Vehicle brakes must convert kinetic energy into thermal energy through friction to stop the vehicle.
2
Calculate the factor change in kinetic energy when speed doubles
When speed increases from vv to 2v2v, kinetic energy increases by (2)2=4(2)^2 = 4 times.
Doubling velocity quadruples kinetic energy.
3
Relate kinetic energy to required braking distance
Since braking force is limited by surface friction, dissipating four times the energy requires four times the distance.
Work required to stop (W=F×dW = F \times d) equals kinetic energy, so d∝v2d \propto v^2.

Key Concept

Kinetic Energy and Quadrupled Braking Distance
Estimated Time:1m 30s
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Topics

Speed Control and Following Distance

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