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Difficulty: MediumStopping Distance Components

A commercial driver operating a vehicle equipped with an air brake system is traveling on a dry, level roadway at a constant speed of 44 feet per second44\text{ feet per second} (approximately 30 mph30\text{ mph}). The driver takes 1.5 seconds1.5\text{ seconds} to perceive a road hazard and an additional 0.75 seconds0.75\text{ seconds} to apply the brake pedal. The air brake system experiences a 0.5-second0.5\text{-second} brake lag before the brakes engage, after which the vehicle requires 75 feet75\text{ feet} of actual braking distance to come to a complete stop. What is the total stopping distance of the vehicle, in feet?

Answer: 196 feet

Answer

The total stopping distance is 196 feet196\text{ feet}.
For air brake-equipped vehicles, total stopping distance consists of four distinct components: perception distance (44 ft/s×1.5 s=66 ft44\text{ ft/s} \times 1.5\text{ s} = 66\text{ ft}), reaction distance (44 ft/s×0.75 s=33 ft44\text{ ft/s} \times 0.75\text{ s} = 33\text{ ft}), brake lag distance (44 ft/s×0.5 s=22 ft44\text{ ft/s} \times 0.5\text{ s} = 22\text{ ft}), and physical braking distance (75 ft75\text{ ft}). Summing these four distances gives 66+33+22+75=196 feet66 + 33 + 22 + 75 = 196\text{ feet}.

Step-by-Step Solution

1
Calculate the perception distance
Perception Distance = 44 ft/s×1.5 s=66 feet44\text{ ft/s} \times 1.5\text{ s} = 66\text{ feet}
Perception distance is the distance traveled from the moment the hazard appears until the driver identifies it.
2
Calculate the reaction distance
Reaction Distance = 44 ft/s×0.75 s=33 feet44\text{ ft/s} \times 0.75\text{ s} = 33\text{ feet}
Reaction distance is the distance traveled while moving the foot from the accelerator to the brake pedal.
3
Calculate the air brake lag distance
Brake Lag Distance = 44 ft/s×0.5 s=22 feet44\text{ ft/s} \times 0.5\text{ s} = 22\text{ feet}
Air brake systems require air to build pressure in the lines and chambers before the shoes press against the drums.
4
Sum all four components to find the total stopping distance
Total Stopping Distance = 66+33+22+75=196 feet66 + 33 + 22 + 75 = 196\text{ feet}
For an air brake-equipped commercial vehicle, total stopping distance equals Perception Distance + Driver Reaction Distance + Brake Lag Distance + Effective Braking Distance.

Key Concept

Four-component total stopping distance formula for air brake systems: Total Stopping Distance = Perception Distance + Reaction Distance + Brake Lag Distance + Braking Distance.
Estimated Time:1m 30s
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Stopping Distance Components

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