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Difficulty: HardStopping Distance Components

A fully loaded tractor-trailer with an S-cam pneumatic brake system is cruising at a constant speed of 60 mph60\text{ mph} (88 ft/s88\text{ ft/s}) on a dry, level highway. Upon spotting a stalled vehicle ahead, the driver takes 1.75 seconds1.75\text{ seconds} to recognize the hazard (perception phase) and an additional 0.75 seconds0.75\text{ seconds} to move their foot to the brake pedal (reaction phase). The pneumatic system requires 0.50 seconds0.50\text{ seconds} for air pressure to build up and push the brake linings against the drums. If the entire stop from initial hazard recognition to a complete standstill requires a total distance of 470 feet470\text{ feet}, what is the vehicle's effective braking distance (the distance traveled while the brakes are actively slowing the vehicle), in feet?

Answer: 206 ft

Answer

The effective braking distance is 206 ft206\text{ ft}.
Total stopping distance for an air-brake-equipped commercial vehicle consists of four consecutive components: perception distance (1.75 s×88 ft/s=154 ft1.75\text{ s} \times 88\text{ ft/s} = 154\text{ ft}), reaction distance (0.75 s×88 ft/s=66 ft0.75\text{ s} \times 88\text{ ft/s} = 66\text{ ft}), brake lag distance (0.50 s×88 ft/s=44 ft0.50\text{ s} \times 88\text{ ft/s} = 44\text{ ft}), and effective braking distance. Subtracting the combined pre-braking distance of 264 ft264\text{ ft} from the overall stopping distance of 470 ft470\text{ ft} yields an effective braking distance of 206 ft206\text{ ft}.

Step-by-Step Solution

1
Calculate the distances traveled during perception, reaction, and air brake lag phases at the constant speed of 60 mph60\text{ mph} (88 ft/s88\text{ ft/s})
Perception distance = 1.75 s×88 ft/s=154 ft1.75\text{ s} \times 88\text{ ft/s} = 154\text{ ft}; Reaction distance = 0.75 s×88 ft/s=66 ft0.75\text{ s} \times 88\text{ ft/s} = 66\text{ ft}; Air brake lag distance = 0.50 s×88 ft/s=44 ft0.50\text{ s} \times 88\text{ ft/s} = 44\text{ ft}.
Before the friction brakes physically apply stopping force at the wheels, the vehicle continues moving at its initial cruising speed through perception time, driver reaction time, and air line charging time.
2
Sum all pre-braking delay distances
Total Pre-Braking Distance=154 ft+66 ft+44 ft=264 ft\text{Total Pre-Braking Distance} = 154\text{ ft} + 66\text{ ft} + 44\text{ ft} = 264\text{ ft}.
All three delay components occur consecutively while the vehicle maintains unretarded forward travel.
3
Subtract the combined pre-braking distance from the total stopping distance
Effective Braking Distance=470 ft−264 ft=206 ft\text{Effective Braking Distance} = 470\text{ ft} - 264\text{ ft} = 206\text{ ft}.
Total stopping distance for a commercial vehicle with air brakes equals the sum of perception distance, reaction distance, brake lag distance, and effective braking distance.

Key Concept

Total stopping distance for commercial vehicles with air brakes comprises four distinct components: perception distance, reaction distance, brake lag distance, and effective braking distance.
Estimated Time:2m 0s
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Topics

Stopping Distance Components

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