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GATE 2017 CE (CE2) – Question 46

Traffic Engineering and Transportation Planning · Fundamental relationships of traffic flow · 2 marks · Multiple choice

Two cars P and Q move for two hours with distances (km) $d_P=60t$, $d_Q=60t^2$, where t is hours. Their maximum headway in the first hour and its occurrence time are ______.

  1. 15 km, 30 min
  2. 15 km, 15 min
  3. 30 km, 30 min
  4. 30 km, 15 min

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Correct answer: (A) 15 km, 30 min

Explanation

In the first hour, separation is $h=60t-60t^2$. Setting $h^\prime=60-120t=0$ gives $t=0.5$ h; the second derivative is negative. Thus $h=60(0.5-0.25)=15$ km at 30 minutes (A).