Overtaking time on a two-lane highway A vehicle (design speed 50 km/h) accelerates uniformly at 1.25 m/s^2 to overtake a slower vehicle moving steadily at 30 km/h. Estimate the approximate overtaking time required.

Introduction / Context:
Overtaking time is a key parameter in overtaking sight distance (OSD) analysis. It depends on the initial speed differential, acceleration capability of the overtaking vehicle, and the final speed reached while completing the manoeuvre safely.

Given Data / Assumptions:

• Speed of slower vehicle V_s = 30 km/h = 8.33 m/s.
• Design (target) speed V_d = 50 km/h = 13.89 m/s.
• Uniform overtaking acceleration a = 1.25 m/s^2.
• Level road; simple pass without extra clearance allowances (concept check).

Concept / Approach:
A simplified kinematic estimate for the time spent in the active passing phase is based on the speed change needed relative to the slower vehicle. A common approximation assumes the overtaking vehicle accelerates from near the slower vehicle speed up to about the design speed to complete the pass, hence time is driven by the acceleration to gain the additional speed margin.

Step-by-Step Solution:

Verification / Alternative check:
Highway design texts often show passing times of 6–8 s for such speed differentials and modest accelerations; 6.12 s lies within that band.

Why Other Options Are Wrong:
5.0 s underestimates clearance time; 30 s and 225.48 s are unrealistically large for such speeds and accelerations.

Common Pitfalls:
Ignoring acceleration capability; using only relative speed without clearance allowance; mixing km/h with m/s.

Final Answer:
6.12 s