Am I correct in my assumptions?

[rootX]

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?

 

[FedEx]

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?

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).

 

[rootX]

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).

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