Kinetic Energy and Changes in Gravitational Potential Energy Equations

Kinetic Energy is the energy an object has due to its motion. It is directly proportional to an object’s mass and the square of its velocity. The formula for kinetic energy is K.E. = 1/2 m v^2 where ‘m’ represents mass and ‘v’ represents velocity.
The energy due to an object’s position is represented as gravitational potential energy. This energy is related to an object’s height above the Earth’s surface.
Gravitational Potential Energy (G.P.E.) is given by the formula G.P.E. = m g h, where ‘m’ stands for mass, ‘g’ for gravitational field strength (which is approximated to 9.8 N/kg on the earth’s surface), and ‘h’ for height.
Both kinetic and gravitational potential energy are measured in joules (J).
In an isolated system, the total energy remains constant. This is the principle of conservation of energy. If the kinetic energy of an object changes, there will be a corresponding change in its gravitational potential energy.
If an object is lifted or elevated, its gravitational potential energy increases while if it’s lowered or falls, its gravitational potential energy decreases.
If an object speeds up, its kinetic energy increases and if it slows down, the kinetic energy decreases.
When an object is falling freely under gravity, the energy initially stored as gravitational potential energy gets converted into kinetic energy as the object descends.
In such scenarios, ignoring air resistance, the energy conversion is theoretically 100% efficient, i.e., all of the gravitational potential energy is converted into kinetic energy, signifying the conservation of energy principle.
Work done on an object is the result of the applied force causing displacement. It is mathematically represented as the product of the force and the distance moved in the direction of the force. The unit of work done is also measured in joules (J).
The work done on an object can result, and is equivalent, to a change in its energy - either potential, kinetic, or both.
If the net work done on an object results in it accelerating, then the work done raises its kinetic energy and if it results in the object being elevated, it will increase its gravitational potential energy.