I did not say that there was anything magical about it.
I agree that if you derive the formula from that traditional perspective, then the velocity term must be squared in order to get the right energy value.
An old saying goes that, “there is more than one way to skin a cat.”
As a simile, lets say that both of us were going to some city, lets say Seattle as our destination, now you have taken a train and I have taken a car, but we both end up in the same city.
Your calculations are a culmination of other peoples work. The train is being controlled by someone else.
Where as I derived a formula that gives the same result as the one you use. I’m driving the car, and learned to drive by reading the instructions from the previously mentioned book.
Thanks for the link, it contains a good explanation of the traditional way of understanding the solution to the formula. (If you want to go by train.;-)
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