The reason why a bicyclist on a downhill road picks up speed even when he is not pedaling and also find whether this violates the principle of conservation of energy?
In this case, there are two forms of energy involved; potential energy and kinetic energy. When the bicyclist is at the top of a hill, he has potential energy due to his mass. When bicyclist moves, the energy changes its form to kinetic energy due to his motion. Thus, the bicyclist picks speed when he moves downhill even when he is not pedaling.
There is a transformation in the forms of energy which states the principle of energy. Hence, there is no violation of the principle of conservation of energy.