Question: Due to roadwork ahead, the traffic on a highway slows linearly from 55 miles/hour to 15 miles/hour over a 2000-foot stretch of road, then crawls along at 15 miles/hour for 5000 feet, then speeds back up linearly to 55 miles/hour in the next 1000 feet, after which it moves steadily at 55 miles/hour.
(a) Sketch a velocity vector field for the traffic flow.
(b) Write a formula for the velocity vector field v→ (miles/hour) as a function of the distance x feet from the initial point of slowdown. (Take the direction of motion to be i→ and consider the various sections of the road separately.)
(c) Compute div v→ at x = 1000, 5000, 7500, 10,000. Be sure to include the proper units.