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Getting time/distance taken to accelerate/decelerate

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How do I caulculate tne time and distance taken to decelerate? I have tried EVERYTHING related to A=dV/dT but the damn spaceship either stops to soon, to late, not at all, or goes to lightspeed in the oposite direction! A=dV/dT must be correct but it doesnt match the ETA, because the speed changes. How do I find the total distance traveled during dT when going from 0 to X at a fixed acceleration? if anyone complains about not having newtonian physics in my game, I will tell them to shove an apple up ther arse and jump off a tree >: (

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