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I personally would have gone with: because E=0.5mv^2

And by that i mean that energy is a much more intuitive concept than force.

Why is E proportional to v^2? Now THAT’s an interesting question.

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-...

How about this: because there's a mass involved with a non-zero cross section, so velocity is being added to an area, not a point.

Hence v^2 is hiding the complexity of density vs surface area (the law was originally derived by observing steel ball impact craters on a bed of sand vs the height).

0.5 is because only one side hits.

EDIT: And what surface area? Well General Relativity does like to mash up the concept of objects affecting space time due to having energy...

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