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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?

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The concept of Work was defined to make calculations easier, so I think its the first one, i.e. work energy theorem was deliberately derived from newton's laws, and then the concepts were defined, not the other way round.

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Work-energy theorem is a relation between the effect of an external force and the state-change of the open system. So it is much more fundamental than Newton equations. Also: kinetic energy does not require the Newton equations.

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