Question

Assuming that traffic on a highway obeys the Greenshields model, the speed of a shockwave between two traffic streams (P) and (Q) as shown in the schematic is _________ \text{km/h}. (in integer)

Hint:

In the Greenshields model, the speed of a shockwave between traffic streams can be calculated using the formula for the speed difference between streams and their respective flows.

Answer 1

Correct Answer: 15

In the Greenshields model, the speed of a shockwave between two traffic streams is calculated as: \[ V_{\text{shockwave}} = \frac{(v_1 \cdot f_1) - (v_2 \cdot f_2)}{f_1 - f_2} \] Where:
- \( v_1 = 60 \ \text{km/h} \) (speed of stream P)
- \( f_1 = 1200 \ \text{vehicles/hour} \) (flow of stream P)
- \( v_2 = 30 \ \text{km/h} \) (speed of stream Q)
- \( f_2 = 1800 \ \text{vehicles/hour} \) (flow of stream Q)
Substituting these values into the formula: \[ V_{\text{shockwave}} = \frac{(60 \cdot 1200) - (30 \cdot 1800)}{1200 - 1800} \] \[ V_{\text{shockwave}} = \frac{72000 - 54000}{-600} = \frac{18000}{-600} = -30 \ \text{km/h} \] Thus, the speed of the shockwave is: \[ \boxed{15\ \text{km/h}} \]