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Zorluk: ZorSpeed Control and Following Distance

When a driver doubles their vehicle speed from 30 mph30\text{ mph} to 60 mph60\text{ mph}, doubling their time-based following distance from 3 seconds3\text{ seconds} to 6 seconds6\text{ seconds} keeps the physical space (distance in feet) between the two vehicles exactly the same.

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The statement is False. Doubling both the speed and the time gap quadruples the physical following distance in feet, increasing it from 132 feet132\text{ feet} at 30 mph30\text{ mph} (3 seconds3\text{ seconds}) to 528 feet528\text{ feet} at 60 mph60\text{ mph} (6 seconds6\text{ seconds}).
The statement is false because distance equals velocity multiplied by time (D=v×tD = v \times t). When speed doubles (2v2v) and time interval doubles (2t2t), the resulting distance quadruples (4D4D). At 30 mph30\text{ mph}, 3 seconds3\text{ seconds} represents 132 feet132\text{ feet}, while at 60 mph60\text{ mph}, 6 seconds6\text{ seconds} represents 528 feet528\text{ feet}.

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1
Calculate the physical distance covered in feet during a 3-second3\text{-second} following distance at 30 mph30\text{ mph}.
At 30 mph30\text{ mph}, a vehicle travels 44 ft/s44\text{ ft/s}. Over 3 seconds3\text{ seconds}, the distance is 44 ft/s×3 s=132 feet44\text{ ft/s} \times 3\text{ s} = 132\text{ feet}.
Converting miles per hour to feet per second (1 mph≈1.467 ft/s1\text{ mph} \approx 1.467\text{ ft/s}) establishes the baseline spatial gap.
2
Calculate the physical distance covered in feet during a 6-second6\text{-second} following distance at 60 mph60\text{ mph}.
At 60 mph60\text{ mph}, a vehicle travels 88 ft/s88\text{ ft/s}. Over 6 seconds6\text{ seconds}, the distance is 88 ft/s×6 s=528 feet88\text{ ft/s} \times 6\text{ s} = 528\text{ feet}.
Doubling speed doubles the distance traveled per second.
3
Compare the initial and final physical distances in feet.
528 feet=4×132 feet528\text{ feet} = 4 \times 132\text{ feet}. The physical spatial gap quadruples rather than remaining constant.
Spatial distance scales with both speed and time interval (D=v×tD = v \times t), so doubling both variables multiplies the total spatial distance by four.

Anahtar Kavram

Speed, Time, and Distance Relationship in Following Distance
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Konular

Speed Control and Following Distance

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