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Zorluk: Çok zorSpace Ahead and Following Distance

A commercial driver is operating a 65-foot65\text{-foot} tractor-trailer on a dry, straight highway. To precisely comply with the standard commercial driver space management formula for minimum following distance, the driver is maintaining exactly 495 feet495\text{ feet} of space behind the vehicle directly ahead. What is the steady cruising speed of the truck in miles per hour?

Cevap: 45 mph

Cevap

45
The standard space management rule requires 1 second per 10 feet of vehicle length, plus 1 second for speeds 40 mph or greater. A 65-foot truck requires 6.5 seconds base. The 495-foot gap implies a speed over 40 mph, so the total time gap is 7.5 seconds. Speed = Distance / Time = 495 / 7.5 = 66 feet per second. Converting 66 fps to mph (66 * 3600 / 5280) gives exactly 45 mph.

Adım Adım Çözüm

1
Calculate the base following time for a 65-foot vehicle.
6.5 seconds
The standard rule requires 1 second of following distance for every 10 feet of vehicle length.
2
Deduce whether the speed requires the additional 1-second rule.
Total time gap is 7.5 seconds.
If the speed was under 40 mph, the maximum distance would be roughly 380 feet. Since 495 feet > 380 feet, the speed is at least 40 mph, requiring 1 extra second.
3
Calculate the speed in feet per second (fps).
66 fps
Speed equals distance divided by time: 495 feet / 7.5 seconds.
4
Convert the speed from feet per second to miles per hour.
45 mph
Multiply by 3600 seconds/hour and divide by 5280 feet/mile to convert to mph.

Anahtar Kavram

Calculating speed by reverse-engineering the commercial vehicle space management formula and converting units.

Alternatif Yöntem

You can also set up an algebraic equation directly in mph: Distance = (mph * 5280 / 3600) * Time. Thus, 495 = (mph * 1.4667) * 7.5. Solving for mph: 495 = mph * 11.00025, which gives mph = 45.
Tahmini Süre:3m 0s
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Space Ahead and Following Distance

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