How to calculate time to reach fractions of the speed of light when accelerating at 1g

Currently writing a scifi novel and am trying to do the math to establish time frame of the lore. The main points are that in 2068 CE Earth sent a generation ship to colonize Proxima Centauri. They were never heard from again because Earth was destroyed a 25 years later during WW3 and the survivors around the solar system have no means of contact. The main story partly evolves around first contact with what seems to be aliens, but is actually the return of the generation ship's descendants. I am trying to establish a solid timeline for when the generation ship reached Proxima Centauri.

So to the main question: If the ship leaves Sol accelerating at 1 g (9.8 m/s^2), how long would it take them to reach 4.5% the speed of light (13,490,661 m/s)?

I would like an actual equation, however, because I expect i might need to tweek the numbers for future situations in the story. Rounding to 10 m/s^2 and 13.5M m/s is fine, wouldn't mind knowing the difference though.

posted over 4 years ago

TitaniumTurtle‭

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