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## Homework Statement

Consider a space ship that accelerates so that the passengers feel and acceleration equal to that of gravity of the earth’s surface, g. If the space ship undergoes this acceleration for a time T, show that the final velocity is given by:

V=c[1+(c/gT)^2]^(-1/2)

## Homework Equations

F=(gamma^3)ma where gamma= [1-(v/c)^2]^-1/2 (the Lorentz factor)

## The Attempt at a Solution

Since the passengers always feel the acceleration of gravity, you don’t actually feel acceleration you feel the force mg. So at any time the passengers must feel mg so:

mg=(gamma^3)ma

a=g/(gamma^3)

I converted gamma into the function and tried to integrate to obtain V but that’s where I got stuck .

a=g[1-(v/c)^2]^3/2

I trying to integrate with respect to dt but v it self is a dx/dt so I am wierded out by that. I went to the professor and he gave me a hint in which I have to convert adt into another thing using the chain rule (whatever that means).

Somehow I think I have to integrate with respect to dv and have my limit be gT instead of T but iam not sure how to get to there.

Any help is greatly appreciated I have my test this week and I need to get a A :(.

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