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Best Answer bonanova, 25 January 2014 - 05:13 AM

Spoiler for seems like

Go to the full post


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#1 BMAD

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Posted 24 January 2014 - 06:55 AM

Assume there is a one-lane highway with traffic uniformly moving at 65 mph. An accident occurs, causing cars to stop on the highway. After the accident is cleared off the road, the traffic jam persists. Does the traffic jam persist at the same spot where the accident occurred? Why or why not?
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#2 bonanova

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Posted 25 January 2014 - 05:13 AM   Best Answer

Spoiler for seems like


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#3 harey

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Posted 26 January 2014 - 02:05 AM

Spoiler for seems like

There is no mathematical reason for that, yet you are right. Any idea why?


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#4 bonanova

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Posted 26 January 2014 - 02:14 AM

Sure. Drivers traveling at the speed limit or higher brake out of necessity when they encounter a traffic jam. But the same drivers are able to choose their rate of acceleration when they get to the front. Once there, the slowest of the accelerating cars dictates how quickly the cluster disperses.

 

If the traffic density is high enough (think of Los Angeles traffic) a traffic jam sustains itself even when the initial cause is removed. It does not disperse until the traffic density drops below a threshold value and the accretion rate from behind drops below the dispersion rate in front.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#5 harey

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Posted 27 January 2014 - 05:16 PM

Well, I have never been to LA, but I know what happens in Germany. Bus driving 80 km/h, behind a car driving 90 km/h that begins to overtake without caring much about the cars arriving at 160-260 km/h.

 

When it comes to a stop, I often observed that the first pack of 5 cars needs 13 seconds to move, the second pack 12, the third 11 and the remaining 10. As if the drivers on the begin would need more time to take the decision.


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