What is the capacity of the road section, if speed (V) – density (K) study has resulted in a linear relationship V = 60 – 0·5K ?
- A1800Correct
- B7200
- C900
- D3600
Solution
Concept
Capacity from the linear speed–density relation
Formula
qmax = vf · kj / 4
Step-by-step solution
1. V = 60 − 0.5 K ⇒ free-flow speed vf = 60 km/h; jam density when V = 0: kj = 60/0.5 = 120 veh/km. 2. Capacity qmax = vf kj / 4 = 60 × 120 / 4 = 1800 veh/h.
Explanation
Flow q = K V = 60K − 0.5K². Setting dq/dK = 0 gives K = 60 veh/km, V = 30 km/h and qmax = 1800 veh/h.
Why the other options are wrong
7200 is vf × kj (without dividing by 4). 3600 and 900 are 1/2 and 1/8 of that product.
Shortcut
Capacity = vf × kj / 4.
Common mistake
Forgetting to divide by 4.
Correct answer: A) 1800