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why does a bicyclist pick up speed on a downhill road even when he is not pedaling?does this violate the conservation of energy principle?

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The reason why a bicyclist picks up speed on downhill road is because of the effect of gravity and the position of the road. A downhill road is in a slanting position that when a mass or the weight of the cyclist is applied to the bicycle it will cause the bicycle to speed up even without pedaling.

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Because of gravity. Just like falling or going down a slide, when you get to the bottom you're going faster than you were at the beginning. Your other question - I think it does violate it because the energy is not staying constant it's actually building.

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