How to Calculate Peak Speed and Time Dilation for a Relativistic Spacecraft?

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To calculate the peak speed and time dilation for a spacecraft accelerating at 1 G to the halfway point of a journey to another solar system, then decelerating at the same rate, the relevant formulas involve relativistic physics. The spacecraft should be designed to simulate Earth-like gravity during acceleration and deceleration phases. The time dilation experienced by the crew can be calculated using the Lorentz factor, which incorporates the ship's velocity as it approaches relativistic speeds. The discussion references a specific resource for further understanding of the physics involved in such scenarios. Incorporating acceleration into the time dilation formula requires understanding how velocity changes over time during the acceleration phase.
MelissaBlaze
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Hi,
If I want my spacecraft to accelerate at a rate that produces 1 G for a set distance (half way to another solar system) then decelerate at the same rate for the second half of the trip, what formula would I use? I would like to calculate the peak speed of the ship and the time dilation experienced by the crew.

My thoughts are to design the spacecraft so that the crew would experience Earth like 'gravity' while it accelerates, then at the half way point, the ship would flip 180 degrees so the crew would continue to experience the same 'gravity' while it slows for the second half of the trip. I also need to know how much time will pass for the crew. phyzguy gave me the formula for the time dilation but I don't know how to incorporate acceleration over time into it.
 
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