Work Energy Theorem

The WORK-ENERGY THEOREM connects the work done by a force with the resulting change in an object's kinetic energy.

Case I -- a single conservative opposing force: consider a body of mass m, initial speed u, decelerated to final speed v over a displacement s by a constant opposing force F, so the (negative) acceleration is $a=-\frac{F}{m}$. From $v^2-u^2=2(-a)s=-2\frac{F}{m}s$, multiplying throughout by $\frac{m}{2}$ gives $\frac{1}{2}mv^2-\frac{1}{2}mu^2=-Fs$, i.e. the DECREASE in kinetic energy on the left equals the work done BY the opposing conservative force on the right (with appropriate sign) -- exactly the work-energy theorem: change in kinetic energy = work done by the (conservative) force. …