The following C.M. Work-KE theorem can be easily derived from Newton's laws
alone,with no reference to energy flow or conservation:
1) Define a system simply by choosing its member objects, however far they
are spatially separated.
2) Evaluate the external forces on this system, wherever applied.
3) Vectorially add these forces together (just as you would if they were all
acting on a single object) to obtain the net external force on the system.
4) Evaluate the line integral of this net external system force over the
trajectory of the system Center of Mass during some chosen interval of time
(this of course employs the dot product).
5) This line integral is numerically equal to the increment in the system
C.M. translational kinetic energy during the chosen time interval.
P.S. : The theorem says NOTHING about the flow, or exchange, of energy; It
is simply a useful numerical equality.
Because of this, some now call the above line integral "pseudo work". I
regard the qualification “pseudo”as misguided, coming from the
hindsight motivated expectation that work should necessarily include energy
transfer at the point of force application. This expectation does not
come from Newton's laws, but from the First Law of Thermodynamics.