Which cycle path would be more efficiant and why?
Path with steep hills is more efficient. In stop-go path, stopping converts kinetic energy into heat, then energy is spent to generate kinetic energy. Energy lost to heat cannot be recovered and used to accelerate you and the bike. In the steep hills path, energy is used to pay for the potential energy that goes into raising you and the bike to the peak of the first steep hill. One at the top of the hill, you can just coast, converting potential energy into kinetic energy, then letting that kinetic energy carry you up the next steep hill. if the previous steep hill was taller than the current one, you can just coast over the current hill. if it was shorter, then you only need to add more energy to raise you and the bike from the peak of the last hill to the peak of this hill. In the limit that friction and air resistance is negligible, the energetics tells you that the total amount of energy you have to pay is the potential energy needed to climb the tallest hill; no more, no less. The
