I've been studying the work-energy theorem and also how the kinetic energy formula is derived from the equations of motion. It seems like the work-energy theorem is another way to rewrite the motion equations that, this time, are being supported by the second Newton's law to involve forces.
Does knowing the motion equations and Newton's laws generates the concepts of kinetic energy and work throught mathematical manipulation, or is the the work-energy theorem and its mathematical consistency with equations of motion an independent discovery that it just fits what we knew about motion?