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Displacement homework help

  1. Aug 30, 2006 #1
    The displacement 'x' and time 't' of a particle are related as follows:

    t = [tex]\alpha[/tex][tex]x^2[/tex] + [tex]\beta[/tex][tex]x[/tex]
    where alpha and beta are constants
    Find the retardation of the body in terms of 'v'
    Can someone tell me how to do this??
     
    Last edited: Aug 30, 2006
  2. jcsd
  3. Aug 30, 2006 #2

    J77

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    If v is the velocity, you may want to look at differentiating...
     
  4. Aug 30, 2006 #3

    Astronuc

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    Staff: Mentor

    Are the two x's the same dimension, or do they necessarily have the same exponent?

    Otherwise [itex]\alpha x^2\,+\,\beta x^2[/itex] would simply to

    [itex](\alpha\,+\,\beta) x^2[/itex]
     
  5. Aug 30, 2006 #4
    sorry there was not meant to be an exponent for the second 'x'. I have tried differentiating, but keep getting the wrong answer. I got acc = -2(alpha)v^2/[2(alpha)x + beta]is it right?
     
    Last edited: Aug 30, 2006
  6. Aug 30, 2006 #5

    Astronuc

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    Staff: Mentor

    So just to be clear, t = [itex]\alpha x^2\,+\,\beta x[/itex]?

    So differentiating as suggested by J77, would yield

    1 = [itex]\alpha\,(2x)\,\dot{x}\,+\,\beta[/itex]

    Then separate to find v = dx/dt

    If it is [tex]\beta^x[/tex], i.e. ß^x, that is somewhat more complicated.
     
    Last edited: Aug 30, 2006
  7. Aug 30, 2006 #6
    Sorry I dont get it. and what do the dot above the 'x' indicate?? And it is [tex]\beta[/tex]x
    can u please explain?
     
  8. Aug 30, 2006 #7

    Astronuc

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    Staff: Mentor

    [tex]\dot{x}[/tex] = dx/dt = v

    What do you know about retardation? Do you have a definition or expression for it?
     
  9. Aug 31, 2006 #8
    retardation is just negative acceleration right?
    anyway I have progressed. can you check if this is correct?
    a is the acceleration.

    t = [tex]\alpha x^2+ \beta x[/tex]
    1 = [tex]2\alpha xv+ \beta v[/tex]
    0 = [tex]2\alpha(xa + v^2)+\beta a[/tex]

    therfore, a = [tex]\frac{-2v^2}{2 \alpha x + b} [/tex]
     
    Last edited: Aug 31, 2006
  10. Aug 31, 2006 #9

    J77

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    Looks good - but you forgot an alpha on the top :smile:

    (and your beta seems to have become a b)
     
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