A driver travelling at 20\text{ mph} in dry conditions accelerates to 40\text{ mph}. Stand… — UK Driving Theory Test

A driver travelling at $20\text{ mph}$ in dry conditions accelerates to $40\text{ mph}$ . Standard UK Highway Code tables establish that at $20\text{ mph}$ , a car has a thinking distance of $6\text{ metres}$ ( $20\text{ feet}$ ) and a braking distance of $6\text{ metres}$ ( $20\text{ feet}$ ). How do the thinking distance and braking distance change when vehicle speed is doubled to $40\text{ mph}$ ?

A
Thinking distance doubles to $12\text{ metres}$ ( $40\text{ feet}$ ), and braking distance also doubles to $12\text{ metres}$ ( $40\text{ feet}$ )
Thinking distance doubles to $12\text{ metres}$ ( $40\text{ feet}$ ), while braking distance quadruples to $24\text{ metres}$ ( $80\text{ feet}$ )Answer
C
Thinking distance quadruples to $24\text{ metres}$ ( $80\text{ feet}$ ), while braking distance doubles to $12\text{ metres}$ ( $40\text{ feet}$ )
D
Thinking distance remains unchanged at $6\text{ metres}$ ( $20\text{ feet}$ ), while braking distance increases to $36\text{ metres}$ ( $118\text{ feet}$ )

Answer

Thinking distance doubles to

12\text{ metres}

(

40\text{ feet}

), while braking distance quadruples to

24\text{ metres}

(

80\text{ feet}

According to the UK Highway Code, thinking distance increases in direct proportion to speed because the vehicle covers twice as much ground during the driver's reaction time (

6\text{ m} \times 2 = 12\text{ m}

). Braking distance is proportional to the square of the speed (

v^2

), so doubling the speed quadruples the distance required to come to a stop under braking (

6\text{ m} \times 4 = 24\text{ m}

). Combined, they produce the official

40\text{ mph}

total stopping distance of

36\text{ metres}

(

118\text{ feet}

Step-by-Step Solution

Calculate the change in thinking distance when speed increases from

20\text{ mph}

40\text{ mph}

Thinking distance increases from

6\text{ metres}

(

20\text{ feet}

) to

12\text{ metres}

(

40\text{ feet}

), exactly doubling.

Thinking distance is the distance travelled during human reaction time. Assuming a constant reaction time, distance is directly proportional to vehicle speed (

40 / 20 = 2

Calculate the change in braking distance when speed increases from

20\text{ mph}

40\text{ mph}

Braking distance increases from

6\text{ metres}

(

20\text{ feet}

) to

24\text{ metres}

(

80\text{ feet}

), quadrupling by a factor of 4.

Braking distance is governed by kinetic energy (

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

). Doubling speed multiplies kinetic energy by

2^2 = 4

, requiring 4 times the work and braking distance under uniform friction (

4 \times 6\text{ m} = 24\text{ m}

Verify the combined stopping distance against the official UK Highway Code value for

40\text{ mph}

Total stopping distance is

12\text{ m} + 24\text{ m} = 36\text{ metres}

(

118\text{ feet}

Overall stopping distance equals thinking distance plus braking distance.

Key Concept

Distinction between linear scaling of thinking distance and quadratic scaling of braking distance with speed.

Estimated Time:1m 30s

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