When a vehicle's speed is doubled from 30\text{ mph} to 60\text{ mph}, the braking distanc… — DMV Permit Practice Test

When a vehicle's speed is doubled from $30\text{ mph}$ to $60\text{ mph}$ , the braking distance required to bring the vehicle to a complete stop under identical road conditions also doubles.

Answer: Answer

Answer

False. Doubling vehicle speed quadruples the required braking distance due to the quadratic relationship between speed and kinetic energy.

The statement is false because braking distance does not increase proportionally with speed. According to the laws of physics, a vehicle's kinetic energy increases with the square of its speed (

v^2

). When speed doubles, kinetic energy increases four times, requiring four times as much braking distance to come to a complete stop.

Step-by-Step Solution

Analyze the physical relationship between vehicle speed and kinetic energy

Kinetic energy scales with the square of speed (

E_k = \frac{1}{2}m v^2

Braking force must convert all kinetic energy into thermal energy through friction to bring the vehicle to a full stop.

Calculate the factor change in braking distance when speed increases from

30\text{ mph}

60\text{ mph}

Since speed doubles (

2 \times v

), kinetic energy increases by a factor of

2^2 = 4

Work required to stop the car (

F \times d

) is proportional to kinetic energy, meaning braking distance increases fourfold.

Key Concept

Kinetic Energy and Braking Distance Quadratic Relationship

Estimated Time:1m 0s

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