The cars of a roller coaster reach their maximum kinetic energy when at the bottom of the path. When they start rising, the kinetic energy begins to be converted to gravitational potential energy. The sum of kinetic and potential energy in the system remains constant, ignoring losses to friction.
It can be shown that the kinetic energy of an object is equal to the work needed to accelerate an object of mass m from rest to its stated velocity. Having gained this energy during its acceleration, the object maintains this kinetic energy unless its speed changes. The same amount of work is done by the object when decelerating from its current speed to a state of rest.