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Am i right in my assumptions?

  1. Sep 14, 2007 #1
    assume there's a road

    the cars have length of "d" m, and space btw them is "k", and are moving at "di/dt"

    and at some time, ahead of them is blocked trafic, and in there the cars moving @ "do/dt"

    and so i am analyzing portion of the road that has blocked traffic, like how many cars in it @ given time (N(t) = # of cars in that portion of the road)

    so here's what i did:

    flow into my system = de/dt = do/dt-di/dt

    and it takes t0(=k/(de/dt)) seconds for one more car to come in that my section of the road

    and thus
    N(t) = c + [t](1/t0) gives the # of cars in it at given time t where c is the intial number.
    ignoring that floor ceiling function things..
    so i was wondering if all my assumptions are correct?
     
  2. jcsd
  3. Sep 14, 2007 #2

    I am not able to get that why have you taken de/dt=do/dt-di/dt. Your other assumption of the time taken for an another car to enter the system is correct(I hope so).
     
  4. Sep 14, 2007 #3
    I found that in some other problems (involving some liquid entering into a container with di/dt and leaving at do/dt), and so net rate = di/dt-do/dt

    but, I again worked on this problem, and found that it is incorrect to use in this problem because distance btw. fast cars != dist. btw. slow cars


    Thanks though, I also think that the equation looks good enough(with few modifications):

    N(t) = c + [t](di/dt)(1/k) - [t] (do/dt)(1/p)

    where k is the average dist. btw fast cars, and p is avg dist. btw. slow cars
     
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