QUESTION $4$:

On cee day, the traffic is flowing at a descity of $111$ vellkm oe $1$ cere$-$lane highway A froc$-$flow spoed is $120km$ hour and a capacity is $1500$ vehhour for this highway. Assume that a truck with a speed of $40k\frac{m}{h}$ enters the highmay, travels for $2km$ and exits the highway. When the truck enter the highway, all the cars immstizgly bahind the truck and forces to lower their speed to $40k\frac{m}{2}$ Assume the Groctshisids' mosel :ppolies, delemsine the follonsings using the stock wave theary:

$($a$)$ The maximun density $($jum densaty$)$ and the density as capacity.

$($b$)$ The length of the platoon immediately ufter the truck exits.

$($c$)$ The speed of the frunt of the plation affer tiee truck exits.

$($d$)$ The time it would take for the platoon to dissipate after the trock exits. Assume that there is no congestion on the highway furcher domnsream of the exit poumt.