Question

Difficulty: MediumStopping Distance Components

A commercial motor vehicle equipped with an air brake system travels along a dry, level highway at a constant speed of 60 mph60\text{ mph} (88 ft/s88\text{ ft/s}). The driver spots a sudden road hazard with an average perception time of 1.75 seconds1.75\text{ seconds} and takes 0.75 seconds0.75\text{ seconds} of reaction time to move their foot to the brake pedal. The pneumatic air brake system has a brake lag delay of 0.50 seconds0.50\text{ seconds} before air pressure activates the brake shoes, followed by an effective mechanical braking distance of 216 feet216\text{ feet} to bring the truck to a complete stop. What is the total stopping distance of the vehicle in feet?

Answer: 480 feet

Answer

480 feet
Total stopping distance for an air-brake commercial motor vehicle is calculated using the formula: Total Stopping Distance=Perception Distance+Reaction Distance+Brake Lag Distance+Braking Distance\text{Total Stopping Distance} = \text{Perception Distance} + \text{Reaction Distance} + \text{Brake Lag Distance} + \text{Braking Distance}. At 60 mph60\text{ mph} (88 ft/s88\text{ ft/s}), the truck covers 154 ft154\text{ ft} during perception (1.75 s1.75\text{ s}), 66 ft66\text{ ft} during driver reaction (0.75 s0.75\text{ s}), and 44 ft44\text{ ft} during pneumatic brake lag (0.50 s0.50\text{ s}). Adding these pre-braking distances (264 ft264\text{ ft}) to the mechanical braking distance (216 ft216\text{ ft}) yields exactly 480 feet480\text{ feet}.

Step-by-Step Solution

1
Calculate perception distance
154 feet
At 88 ft/s88\text{ ft/s}, the truck travels for 1.75 s1.75\text{ s} before the driver consciously sees and identifies the hazard (88×1.75=154 ft88 \times 1.75 = 154\text{ ft}).
2
Calculate reaction distance
66 feet
The vehicle continues at full speed for 0.75 s0.75\text{ s} while the driver physically moves their foot onto the brake pedal (88×0.75=66 ft88 \times 0.75 = 66\text{ ft}).
3
Calculate air brake lag distance
44 feet
Air brakes require roughly 0.50 s0.50\text{ s} for compressed air to flow through the lines to the brake chambers before mechanical friction begins (88×0.50=44 ft88 \times 0.50 = 44\text{ ft}).
4
Add the mechanical braking distance to the pre-braking distances
480 feet
Total stopping distance is the sum of Perception Distance (154 ft154\text{ ft}) + Reaction Distance (66 ft66\text{ ft}) + Brake Lag Distance (44 ft44\text{ ft}) + Braking Distance (216 ft216\text{ ft}), giving 154+66+44+216=480 feet154 + 66 + 44 + 216 = 480\text{ feet}.

Key Concept

Total stopping distance for commercial vehicles equipped with air brakes includes four distinct sequential components: perception distance, reaction distance, air brake lag distance, and active mechanical braking distance.
Estimated Time:1m 15s
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