Acceleration/deceleration questions

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SUMMARY

This discussion focuses on the physics of space travel, specifically calculating the time and distance required for a spaceship to reach relativistic speeds (0.9c, 0.92c, and 0.95c) under constant acceleration of 1g. The onboard and off-ship times are derived using the relativistic rocket equations, which are essential for understanding the effects of acceleration on time dilation and distance traveled. Key formulas mentioned include gt= v/√(1-v²) and x= (√(1+g²t²)-1)/g, which provide the necessary calculations for these scenarios.

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  • Understanding of special relativity principles
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  • Knowledge of basic kinematic equations
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JSEBorg
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First of all, a hearty hello to everyone! New poster on this board, though I've been reading this forum quite a bit lately. A bit too much, if you ask my spouse. The questions I want to ask are these:

1) If a ship accelerates at 1g, how long would it take for it to reach .9 of light speed? How much time would've passed, onboard as well as off-ship, until it reaches its cruising speed?
2) How far would that spaceship have traveled from zero to reach .9 the speed of light, if it maintained an acceleration of 1g?

What if you increase the speed to .92 the speed of light - how long will it take (on-board and off-ship) to reach .92? How far would that ship have traveled before reaching that speed?

Or how about .95 the speed of light? How long would it take for a ship to get to that speed at a constant 1g thrust - and again, I'm asking about both on-board-time and off-ship-time. How far would the ship have traveled during this phase to reach "cruising speed"?
 
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[tex]gt=\frac{v}{\sqrt{1-v^2}}[/tex], (with c=1).
[tex]x=\frac{\sqrt{1+g^2t^2}-1}{g}[/tex].
 
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