Since work is positive, the work-energy theorem implies that the kinetic energy has increased. Gravity is a conservative force, however, so the total energy of the system must remain constant. The increase in kinetic energy must therefore be matched by a decrease in potential energy. Since initial potential energy was defined as 0, the potential energy must now be negative, and in fact is equal to
Example:
In order for an object to escape the Earth's gravity, it must achieve a certain escape velocity. A rocket wants to escape to "infinitely far away." Assume that at "infinitely far away," it will have 0 velocity. Any frictional forces may be neglected. The mass of the Earth is km and its radius is m. The gravitational constant
