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Consistent Trajectory for a non-zero rest mass particle?

  1. Feb 9, 2017 #1
    1. The problem statement, all variables and given/known data
    Good day all!
    Quick question:
    As part of a problem statement, i'm asked to verify if the trajectory: [tex] \frac{dx}{dt}=\frac{cgt}{\sqrt{1+g^2t^2}} [/tex]
    Is "consistent".

    2. Relevant equations
    None

    3. The attempt at a solution

    Im not sure what "consistent" means. Does it mean, [itex] \frac {dx}{dt} < c [/itex] for all t? If that's so, I run into a problem because in the limit as t approaches infinity, the velocity = the speed of light (the limit goes to c). Am I approaching this the wrong way? (The trajectory is supposed to be "consistent")
     
    Last edited: Feb 9, 2017
  2. jcsd
  3. Feb 9, 2017 #2

    PeroK

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    You may want to check the limit of that expression for large ##t##.
     
  4. Feb 9, 2017 #3
    PeroK: Not sure what you mean...
    I get "c" as the limit. Maybe my work is wrong? [tex]Lim\, \, t\rightarrow \infty (\frac{cgt}{\sqrt{1+(9.8))^2t^2}})=cg(Lim\, \, t\rightarrow \infty (\frac{t}{\sqrt{1+(9.8))^2t^2}}))=cg(5/49)=c[/tex]. So as t approaches infinity, the velocity approaches c.
     
  5. Feb 9, 2017 #4

    PeroK

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    That's correct, but inconsistent with the limit of ##cg## you gave in the original post!
     
  6. Feb 9, 2017 #5
    Ah, I see. A miss-type. Well, nevertheless, this trajectory doesn't seem to be consistent even though my assignment is saying it should be.
     
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