(CIVL262)[2009](s)quiz4~PPSpider^_10074[1]

# (CIVL262)[2009](s)quiz4~PPSpider^_10074[1] - − = − −...

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CIVL 262 – Introduction to Transportation System Tutorial Quiz 4 6 Mar2009 N a m e : S t u d e n t I D : Shock Waves in Traffic QUESTION 1 A truck with a speed of 12mph enters a traffic stream flowing at 1,000 vehicles per hour and a speed of 50 mph and travels for 2 miles. Because it is impossible to pass, cars immediately behind the truck are forced to match his speed, forming a platoon with concentration of 100 vehicles per mile and moving at a speed of 12 mph. The traffic is then dissipated at an optimal flow of 1,500 vehicles per hour and a speed of 30 mph. a) Calculate the speed of the shock wave at the rear of the platoon. b) What will be the length of the platoon when the truck turns off from the highway? c) How long does it take to clear the platoon after the truck left? Solution: (a) mph k k q q U rear 5 . 2 20 100 000 , 1 200 , 1 1 2 1 2 =
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Unformatted text preview: − = − − = The rear of the platoon is moving forward with a speed of 2.5 mph with respect to the roadway. (b) As the front of the platoon is moving forward with a speed of 12 mph, therefore, the length of the platoon is growing at a rate of (12 - 2.5) = 9.5 mph. Time to travel 2 miles for the truck is hr 6 1 12 2 = , so the length of platoon when the truck turns off is 58 . 1 5 . 9 6 1 ≈ × miles (c) After the truck turns off, the front of the platoon moves with a speed of mph 6 100 50 200 , 1 500 , 1 2 3 2 3 − = − − = − − = k k q q U front The rear of the platoon moves downstream at 2.5 mph and the front of the platoon moves upstream to the rear at 6.0 mph. So time to dissipate the 1.58 miles platoon is 1.58/(2.5+6.0) ≈ 0.186 hr ≈ 11.2 min....
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