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## Homework Statement

Suppose a spaceship starts from rest from a space station floating in deep space and accelerates at a rate of |a| relative to the space station for 1.0 Ms. It then decelerates for the same amount of time at the same constant rate |a| to arrive at rest at another space station and then repeats the trip back to its original space station with the same accelerations. How much less time has passed on the spaceship than on the space station?

Forgot to mention, $$|a| = 10\frac{m}{s^2}$$

Hints: We are supposed to calculate this by breaking the trip into 4 pieces and applying binomial approximation.

## Homework Equations

$$\Delta \tau = \int_{t_A}^{t_B}([1 - v^2])^{(1/2)}$$

## The Attempt at a Solution

I applied binomial theorem and for the first integral I get the following after integrating: $$\Delta \tau_1 = (t - \frac{1}{6}|a|^2t^3) |0Ms, 1Ms$$

The symmetry implies that $$\Delta \tau_1 = \Delta \tau_2 = \Delta \tau_3 = \Delta \tau_4$$ You can check the integrals to make sure this is true. I did, and got the same for each piece. So, $$\Delta \tau = 4 * \Delta \tau_1$$

Now, if you do this on your calculator you should get $$\Delta t - \Delta \tau = 740s$$

The book gets 84s. Either I'm making a mistake, or there is an error in the answers. I usually email the author if I can't see where I could be making a mistake, but I want to clarify with a second opinion before I question his answers.

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