Here's a good explanation (it reduces to F=ma, of course!). This explanation starts by answering a different question, then points out that energy is analogous.

Here's a good explanation (it reduces to F=ma, of course!). This explanation starts by answering a different question, then points out that energy is analogous. https://physics.stackexchange.com/questions/67432/intuitive-meaning-of-factor-2-in-formula-of-vertical-throw-max-height-h-v2-2g/67433#67433 https://physics.stackexchange.com/questions/67432/intuitive-...