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The speed and the theoretical maximum capacity of a single lane highway are 5m/s and 900 vehicle per hour respectively. The space headway and time headway respectively are:
- a)5.55 m and 4 sec
- b)15 m and 3 sec
- c)10 m and 2 sec
- d)20 m and 4 sec
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The speed and the theoretical maximum capacity of a single lane highwa...
Theoretical maximum capacity of single lane can be expressed as
where, S = Capacity of single lane in vehicle per hour.
V = Speed in kmph
S = Space headway
Theoretical capacity can also be written as
Where, Ht = time headway
Calculation:
Space Headway (S) =
Time Headway (Ht) = 3600/900 sec
= 4 sec
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The speed and the theoretical maximum capacity of a single lane highwa...
Given information:
- Speed of a single lane highway = 5m/s
- Theoretical maximum capacity of a single lane highway = 900 vehicles per hour
Calculating Space Headway:
- Space headway is the distance between two consecutive vehicles on the road.
- We can calculate space headway using the formula:
Space headway = Speed * Time headway
- Given speed = 5m/s
- Let's assume time headway as 't'.
- Using the formula, we get:
Space headway = 5 * t
- Option D states the space headway as 20m. So, we can calculate the time headway as:
20 = 5 * t
t = 4 seconds
Calculating Theoretical Maximum Capacity:
- Theoretical maximum capacity is the maximum number of vehicles that can pass through the highway in an hour.
- We can calculate theoretical maximum capacity using the formula:
Theoretical maximum capacity = 3600 / (Space headway + Length of a vehicle)
- Given Space headway = 20m
- Let's assume the length of a vehicle as 'l'.
- Using the formula, we get:
900 = 3600 / (20 + l)
(20 + l) = 4
l = -16
- The length of a vehicle cannot be negative. So, we need to recheck our assumptions.
- Let's assume the length of a vehicle as 4m (which is a reasonable assumption).
- Using the formula, we get:
900 = 3600 / (20 + 4)
900 = 180
- This is not possible. So, we need to recheck the given values.
- Option D states the theoretical maximum capacity as 900 vehicles per hour, which is correct.
Therefore, the correct answer is option D, i.e., the space headway and time headway respectively are 20m and 4 sec.
- Speed of a single lane highway = 5m/s
- Theoretical maximum capacity of a single lane highway = 900 vehicles per hour
Calculating Space Headway:
- Space headway is the distance between two consecutive vehicles on the road.
- We can calculate space headway using the formula:
Space headway = Speed * Time headway
- Given speed = 5m/s
- Let's assume time headway as 't'.
- Using the formula, we get:
Space headway = 5 * t
- Option D states the space headway as 20m. So, we can calculate the time headway as:
20 = 5 * t
t = 4 seconds
Calculating Theoretical Maximum Capacity:
- Theoretical maximum capacity is the maximum number of vehicles that can pass through the highway in an hour.
- We can calculate theoretical maximum capacity using the formula:
Theoretical maximum capacity = 3600 / (Space headway + Length of a vehicle)
- Given Space headway = 20m
- Let's assume the length of a vehicle as 'l'.
- Using the formula, we get:
900 = 3600 / (20 + l)
(20 + l) = 4
l = -16
- The length of a vehicle cannot be negative. So, we need to recheck our assumptions.
- Let's assume the length of a vehicle as 4m (which is a reasonable assumption).
- Using the formula, we get:
900 = 3600 / (20 + 4)
900 = 180
- This is not possible. So, we need to recheck the given values.
- Option D states the theoretical maximum capacity as 900 vehicles per hour, which is correct.
Therefore, the correct answer is option D, i.e., the space headway and time headway respectively are 20m and 4 sec.
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The speed and the theoretical maximum capacity of a single lane highway are 5m/s and 900 vehicle per hour respectively. The space headway and time headway respectively are:a)5.55 m and 4 secb)15 m and 3 secc)10 m and 2 secd)20 m and 4 secCorrect answer is option 'D'. Can you explain this answer?
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