Nice-ish analysis, and as far as they go the equations are correct and the explanations too. BUT, the minor quibble, these Newtonian equations simply don’t apply at relativistic speeds, so plugging in v=c is balderdash. The major quibble is that the limiting condition is not v= v_e, but arises from the maximum normal reaction -the so called g-force- and their duration and direction. Assuming for simplicity that we ignore direction, vibrations and duration, the maximum is about 5g for the average human body. Use that. The mechanical stresses then produced are well within mechanical engineering range.

If readers want to delve deeper, go read a book published by Scientific American in the 70s or 80s on Amusement Park Physics, which talks about the jerk vector or rate of change of acceleration as the primary determinant of the “thrill”.

I stop to miau to cats.

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