why does a cycle stop when we stop paddling or why does it move on paddling?

Its very simple. FRICTION !!!!!!!!!!

Friction is constantly acting on the tires. Due to friction, there is a retarding force. Due to this the cycle keeps decelerating if you dont paddle. When you paddle, you apply force on the wheels, causing friction to act in the direction of motion.

Friction ALLOW the cycle to move because  when the u paddle, the wheel exert force on ground and by newton's third law the ground pushes u back ( which is only possible with friction - imagin runnin on ice where there is not much friction) and give you the forward movement.                      At the same time resistive firction also act against ur motion so u will be in a constant velocity.

But once you stop paddling no more force is exerted, so, no force pushing you forward. while resistive frictional force will continue act against you causing your cycle to stop