Oh my god!!! 42 minutes! *42*!!!! The meaning of the universe revealed!!!!!!

Nice!

It's wrong. As you travel further down the hole, atmospheric pressure will increase, causing increasing drag. Eventually the air will liquefy under intense pressure. You will be foreever stuck in the depths of the Earth. In fact, I believe the pressure and temperature would solidify the atmosphere at a certain depth; prior to which you are traveling pretty slow due to the drag of liquefied air, so you will just come to a stop there. Before you got there, increasing temperatures would have caused your body to decompose, much of which is water which would become solid under this extreme temperature/pressure. You will be mostly just "snow" fluttering slowly down through the hot liquid "air" landing gently on the solid surface deep within the Earth. Or perhaps you will never get that far down due to churn from the heat further down causing strong currents going up and down the tunnel-- you will just be debris swirling forever in those currents.

simple solution, make the tube a vacuum, no air resistence and nothing to solidify, plus the practical tubes wouldn't be straight through, they would be like in the video, new york to paris, paris to moscow, that way you never pass through the actual earths core

I dunno, I think terminal velocity is also to account. I don't think that you will continually accelerate the whole time you will reach a speed where you don't travel faster and then you won't have enough force to propel up the other end... Maybe some sort of electromagnetic forces to carry the cart up the rest of the way... of course then again in a vacuum i'd be mistaken because terminal velocity is dependent on air resistance... but it seems unrealistic to vacuum seal a 7000 mile long tube every travel. I've always been curious about this