Consider a particle in hyperbolic motion, (a) Find the

Chapter 12, Problem 28P

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QUESTION:

Problem 28P

Consider a particle in hyperbolic motion,

(a) Find the proper time τ as a function of t, assuming the clocks are set so that τ = 0 when t = 0. [Hint: Integrate Eq. 12.37.]

(b) Find x and v (ordinary velocity) as functions of τ .

(c) Find ημ (proper velocity) as a function of τ .

Reference equation 12.37

Questions & Answers

QUESTION:

Problem 28P

Consider a particle in hyperbolic motion,

(a) Find the proper time τ as a function of t, assuming the clocks are set so that τ = 0 when t = 0. [Hint: Integrate Eq. 12.37.]

(b) Find x and v (ordinary velocity) as functions of τ .

(c) Find ημ (proper velocity) as a function of τ .

Reference equation 12.37

ANSWER:

Solution 28P

Step 1 of 4:

  1. We need to find out the proper time  as a function of .

Consider a particle travelling in hyperbolic motion,

                                 ,

        Then

                                

                                

                                

                                

                                

We know that,

                                                

                                

                                

                                

And,

                                

                                

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