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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).
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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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