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A single-lane highway has a traffic density of 40 vehicles km If the time-mean speed and space-mean speed are 40 kmph and 30 kmph, respectively, the average headway (in seconds) between the vehicles is
  • a)
    2.25
  • b)
    6.25 x 10-4
  • c)
    3.00
  • d)
    8.33 x 10-4
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A single-lane highway has a traffic density of 40 vehicles km If the t...
q = kV
q = Flow of traffic (veh/m)
V = Space mean speed of vehicle
k = Density of traffic (veh/km)
∴  q = 40 x 30 = 1200 veh/hr
∴ q = 3600/ht1   
∴ ht = 3 sec.  (time headway)
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Community Answer
A single-lane highway has a traffic density of 40 vehicles km If the t...
**Given data:**
- Traffic density = 40 vehicles/km
- Time-mean speed = 40 km/h
- Space-mean speed = 30 km/h

**To find:**
- Average headway between the vehicles

**Formula:**
Headway (H) = 1 / (Traffic density)

**Calculations:**
Given traffic density = 40 vehicles/km

So, headway (H) = 1 / 40 = 0.025 km/vehicle

To convert km/h to km/s, divide by 3600 (since 1 hour = 3600 seconds).

Time-mean speed = 40 km/h = (40/3600) km/s = 0.0111 km/s

Space-mean speed = 30 km/h = (30/3600) km/s = 0.0083 km/s

Now, we know that headway (H) = Space-mean speed / Time-mean speed

Substituting the given values, we get:

H = 0.0083 km/s / 0.0111 km/s

H = 0.7477 seconds

Rounding off to two decimal places, the average headway between the vehicles is approximately 0.75 seconds.

Therefore, the correct answer is option 'C' - 3.00 seconds.
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A single-lane highway has a traffic density of 40 vehicles km If the time-mean speed and space-mean speed are 40 kmph and 30 kmph, respectively, the average headway (in seconds) between the vehicles isa)2.25b)6.25 x 10-4c)3.00d)8.33 x 10-4Correct answer is option 'C'. Can you explain this answer?
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