I am new on this forum and I really really need your help hope that i did post my problem in the good forum.
I am doing a master in transport and I have this exercice to do:
one a one-way carriageway, the relation between space mean speed Vs (km/h) and density k (veh/km) is: Vs=v0exp(-k/km), where v0=100km/h.
The relation between flow q and density k is q=kv for heterogeneous traffic and q=k.Vs for heterogeneous traffic, so q=k.v0exp(-k/km).
I have to find by differentiation k but I am lost. I tried everything but cannot find k. k is suppose to be equal to 50.
Could you help or guide me a bit.
It is not entirely clear what you wish to do.
I don't know the physics behind the question in detail, but I know how to differentiate. When you say that you want to find k by differentiation, I suppose you want to find a value of k that makes some function maximal or minimal? And a second question, exactly which of the given functions do you wish to differentiate?
I want to differentiate all that equation with the values I gave above:
q=k.v0exp(-k/km). v0= 100 and km=50.
Hope it is clear now.
To differentiate with respect to k then use the product rule with and (chain rule)