How to derive kinetic energy Ek=1/2mv^2?

Question

Suppose that you don't know that the relation,
mechanical work W=F.S.

In this circumastances can you derive the equation Ek=1/2mv^2 (without using the relation W=F.S)?

I think any of the two relation (W=F.S and Ek=1/2mv^2) is axiomatic and they are circular. So that you can't get one of them without using the other. When one of them is defined axiomaticaly you can get the other.
Am I correct? please inform me!!

Answer 1

The fact that you can derive one from the other doesn't make them "circular." A circular argument is one in which you assume your conclusions. Circular arguments are invalid, but not reversible derivations.

Work and KE are only defined because they are useful. If you knew absolutely noting about force, you would still define the same KE because it is a conserved quantity.

In real life physics, there is no force (because its definition *is* circular), and conserved quantities are the results of group symmetries. For every symmetry in the system, you derive a conservation law. If the system is time-symmetric (potentials do not vary with time) then energy is conserved. So in real life KE is derived directly from a basic axiom and you forget about work.