# Necessity of the Notion of Work and Kinetic Energy

I've worked through many example problems in my college physics text in the section on kinetic energy and work. I noticed that if the desired quantity is velocity or force, they can be solved entirely with kinematics formulas and the second law. For non-constant acceleration, the acceleration function can be appropriately integrated to solve for velocity and distance with appropriate initial conditions.

So is the work and kinetic energy concepts needed, if one is only after distance, velocity and force? If yes, please provide an example where energy and the work-kinetic energy theorem must be used to solve it.

Suppose the Moon stops abruptly in its orbit around the Earth. Let $T_f$ be the time it would take to the Moon to fall on Earth, and let $T_o$ be the original orbital period of the Moon around the Earth. Determine the ratio $T_f/T_o$.