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RE: The Constantly Renewed Generation Ship
The human body can survive any speed, it is acceleration and deceleration that will kill you.
With an antimatter engine you can control the acceleration of the ship. Ideally one Earth gravity would be optimal also known as 1 g or 9.8 m/s2.
Once you reach your target speed turn off the engine and coast. The crew will then experience zero gee until it is time to decelerate and slow down.