Let's say you have a very powerful hypothetical fusion or matter/antimatter drive on a spaceship and you want to travel to a star nearby. Can you get 1g artificial gravity by accelerating? Or close to 1g? The starship will have to turn halfway to decelerate. Anyway, will accelerating/decelerating at relativistic speeds give artificial gravity inside for the whole trip?
The speed of the craft is not a factor in the acceleration felt by the passengers.
If the craft accelerates at 1 g, 1 g is what the passengers will feel, from the moment that the acceleration starts.
There is no current spacecraft engine technology that can produce anywhere near that level of acceleration for long periods of time.