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among the two paths what will be the easier path to ride cycle. enter image description here

  1. Riding it in an overhead bridge by pedaling when going up and letting cycle free when coming down.
  2. riding it on a flat road and traveling the same displacement as in the first case.

consider driving in a practical situation i.e., with friction between wheels and road, with air drag, etc....

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    $\begingroup$ Hint: cycling is more popular in Holland than in Switzerland $\endgroup$ – RogerJBarlow May 27 '18 at 12:00
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Path 2 is "better" in terms of both energy consumed and comfort.

  1. Energy -- Work done by gravity is same in both cases, so let's ignore that. Looking at energy lost due to friction and air drag -- work done by friction and air drag depends on path and path 1 is longer. Plus, you'll need to brake when going downhill so as to not go too fast. Energy is wasted there. So, overall less energy is wasted in path 2.
  2. Comfort -- Firstly, it is harder to go uphill than on a plain road; I know, I know, there's a downhill part as well on path 1, but then you need to maintain your speed using brakes. Secondly, path 2 is shorter so the time taken will be less if speed is same on both paths.
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