The question is to figure out how the energy can be derived knowing just one thing:
There is a quantity called Energy that is conserved over time.
The goal is to get an equation that somehow implies the basic formulas for kinetic energy and potential energy, $\frac{1}{2}mv^2$ and $mgh$. So how can we get this with just a rudimentary knowledge of physics and algebra, and the first principle (stated above)?
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