Is it possible to solve for “t?”

[etotheipi]

I don't think you can. In any case the mathematical solution is useless, this is an engineering problem and yopu need to non-neglect all the neglected variables.

The resulting problem is only solvable (but trivially solvable) by computational methods.

There is nice approximate form of solution starting on bottom of 332 here:
https://www.jstor.org/stable/2974953?seq=5#metadata_info_tab_contents

Also, I think this is not an engineering problem, but quite a purely mathematical problem!

 

[pbuk]

There's tons of open sourced info about this in Musk's hyperloop project, no need to pursue it further here.

 

[fresh_42]

There's tons of open sourced info about this in Musk's hyperloop project, no need to pursue it further here.

... where still the mathematical formula should be discussed, and not the physical system which led to it.

If someone wants to open a new thread about Hyperloop, please feel free to do so. Contact a mentor if you want some of the late posts here to be moved into the new thread in order to get it started.
This one will be closed.