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Homework Help: A question from a book about relativity

  1. Jul 2, 2010 #1
    1. The problem statement, all variables and given/known data
    Hello ,
    I have a question please , I read in the book ( reflections on relativity ) that :-
    Suppose a particle accelerates in such a way that it is subjected to a constant proper acceleration a0 for some period of time. The proper acceleration of a particle is defined as the acceleration with respect to the particle's momentarily co-moving inertial coordinates at any given instant. The particle's velocity is v = 0 at the time t = 0, when it is located at x = 0, and at some infinitesimal time t later its velocity is t a0 and its location is (1/2) a0 t2. The slope of its line of simultaneity is the inverse of the slope 1/v of its worldline, so its locus of simultaneity at t = t is the line given by
    http://www.m5zn.com/uploads/2010/7/2/photo/0702100307469iwmjeb2nqrkvn4j.bmp
    And my question is how did we derive the last equation ?

    I need help please .



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 2, 2010 #2

    vela

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    That's just the point-slope form of a line:

    [tex]y-y_0 = m(x-x_0)[/tex]

    where the line has slope m and passes through the point (x0,y0). In this case, you have t is in the role of y. Just plug in what the rest of the paragraph tells you and you'll get the derived formula.
     
  4. Jul 4, 2010 #3
    very thanks .
     
  5. Jul 6, 2010 #4
    Please I have another thing here , my book states that :-
    “ This line intersects the particle's original locus of simultaneity at the point (x,0) “
    I can’t understand this statement , please I want someone to explain and prove this statement for me .
    I need help please .
     
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