QUESTION $4$:

Consider traffic flow on a single$-$lane, one$-$way road with a frec$-$flow speed of $50k\frac{m}{h}$our and a

capacity of $1,500ve\frac{h}{h}$our. On one day, vehicles are flowing at a speed of $40k\frac{m}{h}$our. Suddenly,

a large debris falls on the road and blocks the entire lane. Consequently, all the vehicles stop

behind the debris. When the debris is removed $6$ minutes after it falls, the vehicles immediately

start moving again. Determine the followings using the Greenshields' model or the shock wave

theory:

$($a$)$ The jam density and the density at capacity.

$($b$)$ The maximum length of the platoon.

$($c$)$ The time it would take for the platoon to dissipate after the debris is removed. Assume that

there is no congestion on the road further downstream of the vehicle.