Due to roadwork, the traffic on a highway slows linearly from 55 miles/hour to 15 miles/hour over 1500 foot stretch of road, then crawls along at 15 miles/hour for 6500 feet then speeds back up linearly to 55 miles/hour in the next 2000 feet, after which it moves steadily at 55 miles/hour.

(a) Sketch a velocity vector field for the traffic flow. Then write a formula for the velocity vector $\vec v$ (in mi/hr) as a function of the distance $x$ feet along the road from the initial point of slowdown. Take the direction of motion to be $\vec i$ and consider the various sections of the road separately. (For each, write the vector $\vec v$ as a two-dimensional vector; assume that cars do not move perpendicular to the direction of the road.)
For $0 \le x <$ , $\vec v =$
For $\le x <$ , $\vec v =$
For $\le x <$ , $\vec v =$
For $\le x$, $\vec v =$

(b) Find each of the following values of the divergence. For each, include units.
$\mbox{div }\vec v$ at $x = 1000$: $\mbox{div }\vec v =$
$\mbox{div }\vec v$ at $x = 3000$: $\mbox{div }\vec v =$
$\mbox{div }\vec v$ at $x = 9750$: $\mbox{div }\vec v =$