In traffic engineering, estimate the basic (theoretical) capacity of a single lane when the mean speed of vehicles is 24 km/h, the safe stopping distance is 19 m, and the average vehicle length is 6 m. Assume each vehicle occupies a space headway equal to its length plus the stopping distance.

Introduction / Context:Basic lane capacity is a foundational concept in highway capacity analysis. It represents the theoretical maximum flow on a lane when drivers maintain a safe spacing composed of their vehicle length plus the stopping distance at the prevailing speed.

Given Data / Assumptions:

• Mean speed v = 24 km/h.
• Stopping distance = 19 m.
• Average vehicle length = 6 m.
• Space headway = vehicle length + stopping distance.
• Uniform flow without interruptions or lane changing.

Concept / Approach:For uninterrupted, steady flow, the theoretical flow q (vehicles per hour) equals the distance traveled per hour divided by the space required per vehicle. Thus q = (hourly travel distance) / (space headway).

Step-by-Step Solution:

Verification / Alternative check:If drivers reduce spacing slightly or speed increases marginally, 960–1000 vehicles/h is realistic for basic capacity under these assumptions.

Why Other Options Are Wrong:500 and 700 vehicles/h underestimate flow for the given spacing; 1250 vehicles/h would require only 19.2 m per vehicle at 24 km/h, which is below the provided safe spacing.

Common Pitfalls:Forgetting to add vehicle length to stopping distance; mixing units km/h with m/s; applying time headway directly without converting to space headway.

Final Answer:1000 vehicles per hour