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**1. Homework Statement**

A rocket is accelerated for 10 years at a constant rate of 10 m/s². Then starts braking at -10 m/s². Then goes all the way back to its starting point by again first accelerating 10 years at 10m/s² and then braking at the opposite rate for 10 years. How much time has it been for an observer on the resting frame situated on the departure point?

**2. Homework Equations**

The Lorentz boost transformation in the x direction: http://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction

**3. The Attempt at a Solution**

I think a possible solution would be to substitute dt and dt' in the Lorentz transformation for the time coordinate and integrate dt', but I feel like something is wrong here:

[itex]dt' = \gamma(t-\frac{vdx}{c^2}) = \frac{dt-\frac{v}{c^2}\frac{dx}{dt}dt}{\sqrt{1-\frac{v^2}{c^2}}} = \frac{dt-\beta^2 dt}{\sqrt{1-\beta^2}} = \sqrt{1-\beta^2} dt

[/itex]

Can you tell me if I am using the right approach?