31. The relation between speed u (in km/h) and density k (number of vehicles/km) for a traffic stream on a road is u = 70 – 0.7k. The capacity on this road is __________ vph (vehicles/hour).

1. 1. 175

   
   
   

   2. 45

   
   
   

   3. 75

   
   
   

   4. 25

   
   
   

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1. View Hint View Answer Discuss in Forum

   u = 70 – 0.7 k
   Capacity, q = u.k
   ∴ q = (70 – 0.7k)k = 70k – 0.7k²
   

   	dq	= 0
   	dk

   
   ∴ 70 – 0.7 × 2k = 0
   

   ⇒ k =	70	= 50 V / Km
   	0.7 × 2

   
   ∴ q = (70 – 0.7 × 50) × 50 = 175 V/hr

   Correct Option: A

   u = 70 – 0.7 k
   Capacity, q = u.k
   ∴ q = (70 – 0.7k)k = 70k – 0.7k²
   

   	dq	= 0
   	dk

   
   ∴ 70 – 0.7 × 2k = 0
   

   ⇒ k =	70	= 50 V / Km
   	0.7 × 2

   
   ∴ q = (70 – 0.7 × 50) × 50 = 175 V/hr

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32. A two-lane urban road with one-way traffic has a maximum capacity of 1800 vehicles/hour. Under the jam condition, the average length occupied by the vehicles is 5.0 m. The speed versus density relationship is linear. For a traffic volume of 1000 vehicles/hour, the density (in vehicles/km) is
    

1. 1. 52
      

   
   
   

   2. 58
      

   
   
   

   3. 67
      

   
   
   

   4. 75

   
   
   

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1. View Hint View Answer Discuss in Forum

   qmax =	kj.uj
   	4

   
   

   ∴ kj =	4. qmax	=	4 × 1800	= 400 veh. / km
   	uj		18

   
   

   q = k.v = k		uf		1 -	k
   					kj

   
   

   1000 = k		18		1 -	k
   					400

   
   ∴ k = 66.6 ≈ 67.

   Correct Option: C

   qmax =	kj.uj
   	4

   
   

   ∴ kj =	4. qmax	=	4 × 1800	= 400 veh. / km
   	uj		18

   
   

   q = k.v = k		uf		1 -	k
   					kj

   
   

   1000 = k		18		1 -	k
   					400

   
   ∴ k = 66.6 ≈ 67.

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33. Two major roads with two lanes each are crossing in an urban area to form an uncontrolled intersection. The number of conflict points when both roads are one-way is "X" and when both roads are two-way is "Y". The ratio of X to Y is
    

1. 1. 0.25
      

   
   
   

   2. 0.33
      

   
   
   

   3. 0.50
      

   
   
   

   4. 0.75

   
   
   

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1. View Hint View Answer Discuss in Forum

   Conflict points :
   Both roads one way – 6 (x)
   Both roads two way – 24 (y)
   x / y = 6 / 24 = 0.25

   Correct Option: A

   Conflict points :
   Both roads one way – 6 (x)
   Both roads two way – 24 (y)
   x / y = 6 / 24 = 0.25

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34. The cumulative arrival and departure curve of one cycle of an approach lane of a signalized intersection is shown in the adjoining figure. The cycle time is 50 s and the effective red time is 30 s and the effective green time is 20 s. What is the average delay?
    

1. 1. 15 s
      

   
   
   

   2. 25 s
      

   
   
   

   3. 35 s
      

   
   
   

   4. 45 s

   
   
   

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1. View Hint View Answer Discuss in Forum

   In SOS cycle, delay is by red signal.
   

   ∴ Avg. delay =	red light time	=	30	= 15 s
   	2		2

   Correct Option: A

   In SOS cycle, delay is by red signal.
   

   ∴ Avg. delay =	red light time	=	30	= 15 s
   	2		2

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35. An automobile with projected area 2.6 m² is running on a road with speed of 120 km per hour. The mass density and the kinematic viscosity of air are 1.2 kg/m³ and 1.5 × 10–5 m² / s, respectively. The drag coefficient is 0.30. The drag force on the automobile is
    

1. 1. 620 N
      

   
   
   

   2. 600 N
      

   
   
   

   3. 580 N
      

   
   
   

   4. 520 N

   
   
   

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1. View Hint View Answer Discuss in Forum

   FD = CD.A.ρ	V2
   	z

   Correct Option: D

   FD = CD.A.ρ	V2
   	z

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