12.5 The Divergence of a Vector Field OPEN Turned in automatically when due. a Due to roadwork, the traffic on a highway

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12 5 The Divergence Of A Vector Field Open Turned In Automatically When Due A Due To Roadwork The Traffic On A Highway 1 (112.03 KiB) Viewed 97 times

12.5 The Divergence of a Vector Field OPEN Turned in automatically when due. a Due to roadwork, the traffic on a highway slows linearly from 50 miles/hour to 5 miles/hour over 2000 foot stretch of road, then crawls along at 5 miles/hour for 4000 feet then speeds back up linearly to 50 miles/hour in the next 2000 feet, after which it moves steadily at 50 miles/hour. (a) Sketch a velocity vector field for the traffic flow. Then write a formula for the velocity vector ū (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 i and consider the various sections of the road separately. (For each, write the vector ū as a two- dimensional vector; assume that cars do not move perpendicular to the direction of the road.) For 0 < x < 2000 ū= For < x < ū= For < x < v= For < x, ū= (b) Find each of the following values of the divergence. For each, include units. div ū at x = 1500: div v= div v at x = 3000: div V = div ū at x = 7250: div ū=