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Difficulty: MediumStopping Distance Components

A heavy commercial vehicle equipped with air brakes is traveling at a steady speed of 60 mph60\text{ mph} (88 ft/s88\text{ ft/s}) on a level highway. The driver takes 1.75 seconds1.75\text{ seconds} of perception time to identify an upcoming hazard and 0.75 seconds0.75\text{ seconds} of reaction time to move their foot to the brake pedal. An additional 0.5 seconds0.5\text{ seconds} of air brake lag elapses before the air pressure activates the brake shoes. What is the total distance, in feet, traveled by the vehicle during these three phases before mechanical braking begins?

Answer: 264 ft

Answer

264 feet
Total stopping distance in an air-brake-equipped vehicle consists of four parts: perception distance, reaction distance, brake lag distance, and effective braking distance. Before mechanical braking deceleration starts, the truck travels for 1.75 s1.75\text{ s} (perception) + 0.75 s0.75\text{ s} (reaction) + 0.50 s0.50\text{ s} (brake lag) = 3.00 s3.00\text{ s}. At 88 ft/s88\text{ ft/s} (60 mph60\text{ mph}), the total distance traveled during this period is 88 ft/s×3.00 s=264 ft88\text{ ft/s} \times 3.00\text{ s} = 264\text{ ft}.

Step-by-Step Solution

1
Determine the individual component distances for perception, reaction, and air brake lag.
Perception distance = 88 ft/s×1.75 s=154 ft88\text{ ft/s} \times 1.75\text{ s} = 154\text{ ft}; Reaction distance = 88 ft/s×0.75 s=66 ft88\text{ ft/s} \times 0.75\text{ s} = 66\text{ ft}; Brake lag distance = 88 ft/s×0.50 s=44 ft88\text{ ft/s} \times 0.50\text{ s} = 44\text{ ft}.
At a constant velocity of 60 mph60\text{ mph} (88 ft/s88\text{ ft/s}), each phase contributes a distance equal to speed multiplied by time.
2
Sum the three pre-braking distance components.
154 ft+66 ft+44 ft=264 ft154\text{ ft} + 66\text{ ft} + 44\text{ ft} = 264\text{ ft}.
Total distance traveled before the vehicle begins slowing down is the sum of perception distance, reaction distance, and brake lag distance.

Key Concept

Air Brake Stopping Distance Components Prior to Deceleration
Estimated Time:1m 0s
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Topics

Stopping Distance Components

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