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Difficulty: MediumStopping Distance Components

A transit bus fitted with an S-cam pneumatic drum brake system is cruising at 30 mph30\text{ mph} (44 ft/s44\text{ ft/s}) along an urban arterial road. The driver identifies a traffic signal changing unexpectedly to red and executes a full emergency stop. Under standard CDL baseline parameters:
- Perception time is 1.75 seconds1.75\text{ seconds}
- Driver reaction time is 0.75 seconds0.75\text{ seconds}
- Air brake mechanical lag time is 0.50 seconds0.50\text{ seconds}
- The vehicle's mechanical braking distance from the moment the friction linings grip until complete cessation of movement is 88 feet88\text{ feet}

What is the total stopping distance of the bus, in feet, from the point the driver first sees the red signal until the bus reaches a complete stop?

Answer: 220 feet

Answer

The total stopping distance of the bus is 220 feet.
Total stopping distance for an air brake-equipped vehicle is calculated by summing the perception distance (77 ft77\text{ ft}), reaction distance (33 ft33\text{ ft}), air brake lag distance (22 ft22\text{ ft}), and mechanical braking distance (88 ft88\text{ ft}), yielding 77+33+22+88=220 feet77 + 33 + 22 + 88 = 220\text{ feet}.

Step-by-Step Solution

1
Calculate the perception distance by multiplying vehicle speed by perception time.
44 ft/s×1.75 s=77 feet44\text{ ft/s} \times 1.75\text{ s} = 77\text{ feet}
Perception distance is the distance traveled from the instant the hazard appears until the driver's brain recognizes it.
2
Calculate the reaction distance by multiplying vehicle speed by reaction time.
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 the driver physically moves their foot from the accelerator to the brake pedal.
3
Calculate the air brake lag distance by multiplying vehicle speed by brake lag time.
44 ft/s×0.50 s=22 feet44\text{ ft/s} \times 0.50\text{ s} = 22\text{ feet}
Air brake systems require roughly half a second for compressed air to flow through the lines and actuate the brake drums.
4
Sum all four distinct stopping components to compute the total stopping distance.
77 ft+33 ft+22 ft+88 ft=220 feet77\text{ ft} + 33\text{ ft} + 22\text{ ft} + 88\text{ ft} = 220\text{ feet}
For air brake-equipped vehicles, total stopping distance comprises perception distance, reaction distance, air brake lag distance, and effective braking distance.

Key Concept

Total stopping distance in commercial motor vehicles with air brakes consists of four cumulative components: perception distance, reaction distance, air brake lag distance, and mechanical braking distance.

Alternative Method

Sum the total pre-braking delay times first: 1.75 s+0.75 s+0.50 s=3.00 s1.75\text{ s} + 0.75\text{ s} + 0.50\text{ s} = 3.00\text{ s}. Multiply by speed to get the total distance before deceleration begins: 44 ft/s×3.00 s=132 ft44\text{ ft/s} \times 3.00\text{ s} = 132\text{ ft}. Finally, add the mechanical braking distance: 132 ft+88 ft=220 ft132\text{ ft} + 88\text{ ft} = 220\text{ ft}.
Estimated Time:1m 0s
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Stopping Distance Components

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