When a passenger vehicle's driving speed doubles from 30\text{ mph} to 60\text{ mph}, the … — DMV Permit Practice Test

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

Answer: Answer

Answer

The statement is False. When a vehicle's speed doubles, its kinetic energy increases by four times, which quadruples the physical braking distance required to stop under uniform conditions.

The statement is false because braking distance does not increase linearly. Due to the physics of kinetic energy (

E_k = \frac{1}{2}mv^2

), doubling vehicle speed multiplies the kinetic energy by four, thereby requiring four times as much braking distance to absorb that energy under identical road conditions.

Step-by-Step Solution

Identify the relationship between vehicle speed and kinetic energy.

Kinetic energy increases with the square of vehicle speed (

v^2

Vehicle brakes work by converting kinetic energy into thermal energy through friction.

Calculate the factor of change in braking distance when speed doubles.

Scaling speed by a factor of

2

increases kinetic energy by

2^2 = 4

Since work done by friction equals kinetic energy (

F \cdot d = \frac{1}{2}mv^2

), quadrupling kinetic energy requires four times the braking distance

d

Evaluate the statement for truth.

The statement claims braking distance doubles, which is incorrect.

Braking distance quadruples rather than doubles when speed is doubled from

30\text{ mph}

60\text{ mph}

Key Concept

Kinetic Energy and Speed-to-Braking Distance Relationship

Estimated Time:1m 0s

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