The GATE Grind

GATE 2021 CE (CE2) – Question 23

Traffic Engineering and Transportation Planning · Fundamental relationships of traffic flow · 1 mark · Multiple choice

For a negatively sloped linear speed–density relation with free-flow speed vf, at what speed does maximum flow occur?

  1. 0
  2. $v_f/4$
  3. $v_f/2$
  4. $v_f$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $v_f/2$

Explanation

Greenshields’ model gives $v=v_f(1-k/k_j)$ and $q=v_fk(1-k/k_j)$. Setting dq/dk=0 yields k=kj/2. Substituting back gives **v=vf/2 (C)**; free-flow speed occurs at near-zero density, not capacity.