I am Dutch, so I cycle a lot, hence the following question. Say I am standing at the top of a mountain on my bicycle. I have an amount of energy $E$ available. Say that after the slope of the mountain ends, there is an infinite long, straight, smooth road ahead. How do I get the furthest on this flat road? Options:
a) using all my energy $E$ to peddle while I am coming down the mountain
b) roll gently down the mountain and start peddling precisely when I am at the end of the mountain
c) roll gently down the mountain and down the straight road and only when I am starting to get to a hold, I start cycling very slowly, keeping my acceleration and speed to a minimum
d) some kind of hybrid of the above.
In this story I would like to keep it as realistic as possible: there's friction, both from my tires and from air resistance. I once heard that air resistance goes $\propto v^2$, such that I am tempted to opt for option c). I am interested in your opinions/thoughts. Help me spend as little energy as possible while cycling!