The speed-density relationship for a road section is shown in the figure.

Q. The speed-density relationship for a road section is shown in the figure.

The shape of the flow-density relationship is

A. piecewise linear

B. parabolic

C. initially linear then parabolic

D. initially parabolic then linear

Ans: initially linear then parabolic

Sol:

We know, Traffic capacity (q) = velocity (v) × density (k) ⇒ q = kV

For Case 1: When speed is constant, and density of the flow keeps on increasing at the same speed. q = k × constant

∴ Flow becomes the linear function of density and with increase in density, flow increases linearly. For Case 2: With decrease in the speed further, density increases linearly.

Here flow becomes the function the speed as well as density and hence flow becomes the parabolic function of density as density is varying with speed.

∴ After that V varies linearly with k, so q will vary parabolically with k.