Relativistic acceleration transformation

[pantheid]

Homework Statement

The given problem is that we have a rocket ship, accelerating at a constant rate of 1g (in its own instantaneous inertial rest frame) for 40 years. We must find the distance it travels in that time, as measured by an observer on earth.

Homework Equations

dx'=gamma*(dx-vdt)
dt'=gamma*(dt-vdx/c^2)

The Attempt at a Solution

I have derived the relationship a'=a/(gamma^3*(1-uv/c^2)^3)

Given that the rocket has constant acceleration in its own rest frame, a'=g
Given that the observer on Earth is stationary, u=0

If we use these two facts, we get that g*gamma^3=a, which is nonsensical because that means that at very high velocities, the observed acceleration is higher than g when it should be lower. Where is my error?

 

[TSny]

I have derived the relationship a'=a/(gamma^3*(1-uv/c^2)^3)

Given that the rocket has constant acceleration in its own rest frame, a'=g
Given that the observer on Earth is stationary, u=0

I don't believe this is the correct interpretation of u. Make sure you know the meaning of u and v in the formula.