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HJ Farnsworth

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I have been trying to teach myself SR and GR and have been going the Bernard Schutz's First Course in General Relativity to do so. I thought I was understanding all of the concepts perfectly because I have been flying by most of the exercises without having any trouble. However, there are some exercises in the middle of chapter 2 that I have been completely unable to solve, so any conceptual advise would be appreciated. Here are parts of the problems:

19)

A body is said to be uniformly accelerated if its acceleration four-vector a has constant

spatial direction and magnitude, 4-acceleration vector dot 4-acceleration vector = alpha

^{2}.

If a body is uniformly accelerated with alpha=10m/s

^{2}, what is the body's speed after time t?

In trying to solve this, I started by converting alpha to natural units, but don't really know where to go from there. Digging around on the Internet, I've found that I should try to use u=alpha*tau, where u is the proper velocity given by v=tanh(u). I can sort of see how I would solve the problem using this, but I'm not sure how to prove that u=alpha*tau, so I don't want to use it. For that matter, I found on the Wikipedia article for proper velocity that if object B is traveling as observed by Observer A, then proper velocity is A's distance divided by B's time: u=dx

_{obs}/dt

_{obj}. I decided to check if this was consistent with v=tanh(u), and found that it wasn't - the equation I got was u = v/sqrt(1-v

^{2}). My questions for this problem are thus a) how do I prove that v=tanh(u)? b) how do I prove that u=alpha*tau?

20) In some IRF, the worldline of a particle is described by equations:

x(t) = at+bsin(omega*t), y(t) = bcos(omega*t), z(t) = 0, where |b*omega|<1. Find the 4 velocity U and 4 acceleration a.

Basically, I'm having trouble doing this because the the regular 3-velocity isn't constant. Having never done a problem like this before, I'm not sure how to go about it. So I'm just looking for some general tips.

Thank you very much for any help you can give.

-HJ Farnsworth

PS - does the Latex Reference editor generally work for people? Whenever I try to use it, it does stuff that it obviously shouldn't do, like putting individual Greek letters on their own line, or deleting the symbol I use for a vector when I try to put an arrow over it, and then putting the arrow on its own line. Does this website have a better tool for entering equations anywhere?