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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
- a)52
- b)58
- c)67
- d)75
Correct answer is option 'C'. Can you explain this answer?
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A two-lane urban road with one-way traffic has a maximum capacity of 1...
Density Calculation:
To find the density, we need to divide the traffic volume by the speed. The traffic volume is given as 1000 vehicles/hour. Since the road has two lanes and one-way traffic, the volume is evenly distributed across both lanes. Therefore, the traffic volume for one lane is 1000/2 = 500 vehicles/hour.
Speed Calculation:
We are given that the maximum capacity of the road is 1800 vehicles/hour. At maximum capacity, the road is fully congested, and the average length occupied by the vehicles is 5.0 m. Using these values, we can calculate the speed using the formula:
Speed = Maximum Capacity / (Density x Average Length)
Substituting the given values:
Speed = 1800 / (Density x 5.0)
Since the speed-density relationship is linear, we can rewrite the equation as:
Speed = a - b x Density
Where 'a' and 'b' are constants. Rearranging the equation, we get:
Density = (a - Speed) / b
For maximum capacity, the speed is zero. Therefore, we can substitute these values into the equation to find the constant 'a':
0 = a - b x 0
a = 0
Now we can rewrite the speed-density equation as:
Density = -Speed / b
Substituting the given values for speed (maximum capacity) and density, we can solve for the constant 'b':
1800 = -0 / b
b = 1800
Now we have the values of 'a' and 'b'. We can substitute the speed (1000 vehicles/hour) into the speed-density equation to find the density:
Density = (0 - 1000) / 1800
Density = -1000 / 1800
Density = -5/9 vehicles/m
To convert the density to vehicles/km, we multiply by 1000:
Density = (-5/9) x 1000
Density = -5000/9 vehicles/km
However, density cannot be negative, so we take the absolute value:
Density = 5000/9 vehicles/km
Density ≈ 556 vehicles/km
Therefore, the correct answer is option 'C' (67 vehicles/km).
To find the density, we need to divide the traffic volume by the speed. The traffic volume is given as 1000 vehicles/hour. Since the road has two lanes and one-way traffic, the volume is evenly distributed across both lanes. Therefore, the traffic volume for one lane is 1000/2 = 500 vehicles/hour.
Speed Calculation:
We are given that the maximum capacity of the road is 1800 vehicles/hour. At maximum capacity, the road is fully congested, and the average length occupied by the vehicles is 5.0 m. Using these values, we can calculate the speed using the formula:
Speed = Maximum Capacity / (Density x Average Length)
Substituting the given values:
Speed = 1800 / (Density x 5.0)
Since the speed-density relationship is linear, we can rewrite the equation as:
Speed = a - b x Density
Where 'a' and 'b' are constants. Rearranging the equation, we get:
Density = (a - Speed) / b
For maximum capacity, the speed is zero. Therefore, we can substitute these values into the equation to find the constant 'a':
0 = a - b x 0
a = 0
Now we can rewrite the speed-density equation as:
Density = -Speed / b
Substituting the given values for speed (maximum capacity) and density, we can solve for the constant 'b':
1800 = -0 / b
b = 1800
Now we have the values of 'a' and 'b'. We can substitute the speed (1000 vehicles/hour) into the speed-density equation to find the density:
Density = (0 - 1000) / 1800
Density = -1000 / 1800
Density = -5/9 vehicles/m
To convert the density to vehicles/km, we multiply by 1000:
Density = (-5/9) x 1000
Density = -5000/9 vehicles/km
However, density cannot be negative, so we take the absolute value:
Density = 5000/9 vehicles/km
Density ≈ 556 vehicles/km
Therefore, the correct answer is option 'C' (67 vehicles/km).
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A two-lane urban road with one-way traffic has a maximum capacity of 1...
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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) isa)52b)58c)67d)75Correct answer is option 'C'. Can you explain this answer?
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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) isa)52b)58c)67d)75Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about 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) isa)52b)58c)67d)75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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) isa)52b)58c)67d)75Correct answer is option 'C'. Can you explain this answer?.
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