text: can biking on uneven terrain be faster than on flat? assume a flat course on which a biker can average 30 kilometers per hour, if putting his maximal effort. now assume the same biker goes on a terrain the same length, half way uphill and half way downhill (ending in the same location where he started). could he obtain a better time on the second course? like if he is able to maintain an average of 20 km/h uphill the bike would propel him at more than 45 km/h downhill? according to the conservation of energy, your answer is negative. the effort that biker put in each case is consumed to resist both the friction and the work needed against gravity. on flat path, no vertical work is made so his energy (name it e) is totally consumed for resisting friction (f) against movement of him (m) and his bike (m) along the path (l): e=(m+m)*g*f*l now suppose a terrain path (ll) which is surely longer than the straight one (l) which have a max vertical difference of h. the work he must do to move to the top is (m+m)*g*h plus the work needed against alongside friction. the energy will change back to kinetic form during descend session, and therefore cancels the initial effort put. the only work that is to be done is resisting against friction over the longer path, which is certainly more than the straight (shortest) path.