The relation between speed u (in km/h) and density k (number

The relation between speed u (in km/h) and density k (number of vehicles/km) for a traffic stream on a road is u = 70 – 0.7k. The capacity on this road is __________ vph (vehicles/hour).

u = 70 – 0.7 k
Capacity, q = u.k
∴ q = (70 – 0.7k)k = 70k – 0.7k²

	dq	= 0
	dk

∴ 70 – 0.7 × 2k = 0

⇒ k =	70	= 50 V / Km
	0.7 × 2

∴ q = (70 – 0.7 × 50) × 50 = 175 V/hr