# Vacuum travel formula creation

yrh
Say we have a maglev train travelling i a vacuum. The only thing limiting its speed is the g-force tolerance of the passengers.

The train would therefore accelerate at a certain rate until halfway, and then decelerate until it reached its destination.

What would be the travelling time of such a train as a function of the distance?

pseudophonist
$$t=\sqrt{\frac{4s}{g}}$$
where t is the time, s is the distance and g is the accelleration.
Calculated using the fact that distance travelled is the area underneath a velocity-time graph.

yrh
Thank you.

What acceleration value g should I use? I'm looking for an acceleration/deceleration that is hardly noticeable for the passengers, making the journey comfortable.

torquil
With an acceleration of 0.5m/s^2 you can cross the USA in 1.5h in a straight line, which is pretty good...

The chairs could turn 180 degrees when the train is going to decelerate. The top speed would be 2.7km/s.

The usual problem with trains is that they start and stop at all the intermediate stations...

uros
Say we have a maglev train travelling i a vacuum. The only thing limiting its speed is the g-force tolerance of the passengers.

The train would therefore accelerate at a certain rate until halfway, and then decelerate until it reached its destination.

What would be the travelling time of such a train as a function of the distance?

At the distance x the train is accelerated until x/2 so the time is expressed as:
x/2=gt²/2
t=√x/g