Gravities: Just how much acceleration and deceleration can you take? Math pros, need your help on this one

I was reading another tidbit from Leo, and in it he describes a train that travels 2000 k/hr. It uses the “inertial dampeners” to solve the human body turning into puddles problem of acceleration, but I thought, what if you didn’t have IDs to make the ride all cushy and stuff?

Right. The typical human body doesn’t take sustained gravity loads over 1 very well. We know this from research, not the nazis throwing prisoners in a cold pool kind, but US Air Force volunteer kind. And no, not the volunteer to stand next an atomic blast and charge into it after it happens kind of volunteering. (Don’t worry, it’s perfectly safe. That cancer you got is from smoking, not running into a recent nuclear explosion.) Right. There were some messed up things happening in the 40s and 50s, just sayin’.

Take a look here to see a nice article about gravities and your body. Okay, back?

Let’s do some math, then. If you have a train that travels at a maximum of 2000 km/hr, and it travels 6000 km, it should take 3 hours. However, there is acceleration and deceleration, so how long does it take to accelerate to 2000 km if you stay within a 1 gravity limit?

I’ll probably get this wrong, and you can correct me and say, “I see that you never made it past college algebra.”

Okay, so if the gravitational constant of 1 g = 35 km/h^2, then you can safely accelerate at 35 km per hour per second, right? That means it would take one minute of acceleration to reach 2000 km/hr, and there’s probably a nice excel formula that would figure out the distance traveled with a for next statement that run the formula 57 times, adding 35 km/hr to the count each time and the overall distance traveled. Thus, at one second, you are going 35 kph, and in that one second you travel 9.72222 meters. In second 2, you’re going 70 kph, and you travel an additional 19.444 meters. At the end of it, you hit 2000 km/h at second 58 and you’ve traveled 16.68 km.  Let’s pretend deceleration is the same, so you will need those two minutes which will cover only 33.36 km. The rest of the time, you’re doing 2000 km/hr or 555 m/s.  This translates to a travel time of 181 minutes, more or less. Are the inertial compensators necessary?  I must have done something wrong with the rate of acceleration, because this doesn’t look quite right. Is increasing by 35 kph per second = gravitation acceleration?

I think I’m out of my pay grade on this one.

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