Under standard test conditions on a flat, dry asphalt surface, a passenger car moving at 3… — UK Driving Theory Test

Under standard test conditions on a flat, dry asphalt surface, a passenger car moving at $30\text{ mph}$ ( $48\text{ km/h}$ ) achieves an average braking distance of $14\text{ metres}$ ( $45\text{ feet}$ ). If the vehicle accelerates to $60\text{ mph}$ ( $96\text{ km/h}$ ) on the same road surface, what will its new braking distance be, and what physical principle explains this result?

A
28 metres, because braking distance increases in direct linear proportion to vehicle speed
56 metres, because doubling the speed quadruples the kinetic energy that the braking system must absorbCevap
C
42 metres, because overall stopping distance requirements triple when moving into higher speed brackets
D
140 metres, because high speeds reduce tyre contact grip by a factor of ten on dry asphalt

Cevap

56 metres, because doubling the speed quadruples the kinetic energy that the braking system must absorb

Braking distance is proportional to the square of the vehicle's speed (

d \propto v^2

) because kinetic energy increases with the square of velocity (

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

). When speed doubles from 30 mph to 60 mph, the kinetic energy that the brakes must convert into heat increases fourfold (

2^2 = 4

). Consequently, the braking distance quadruples from 14 metres to 56 metres.

Adım Adım Çözüm

Determine the speed scaling ratio

The vehicle speed increases from

30\text{ mph}

60\text{ mph}

, representing a factor of

2\times

Establishing the velocity multiplier is required before evaluating its impact on stopping dynamics.

Apply the kinetic energy equation to determine the braking distance multiplier

Kinetic energy is calculated as

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

, meaning energy increases by

2^2 = 4\times

The vehicle's brakes must perform work equivalent to its kinetic energy to bring it to a complete stop, making braking distance proportional to velocity squared.

Calculate the resulting braking distance

14\text{ metres} \times 4 = 56\text{ metres}

Multiplying the base braking distance by the kinetic energy factor gives the exact new distance required.

Anahtar Kavram

Braking distance is directly proportional to the square of the vehicle's speed (

d \propto v^2

) due to kinetic energy scaling.

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

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