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Particle Dynamics Problem

  1. Feb 2, 2007 #1
    1. A particle is moving along a straight line such that its acceleration is defined as a=(4s^2)m/s^2, where s is in meters. If v=-100m/s when s=10m and t=0, determine the particles velocity as a function of position.

    2. V=ds/dt a=dv/dt

    3. V=ds/dt a=dv/dt 1/dt=ads*vdv
    Integral 100 to s 4s^2ds=Integral -100 to v vdv

    Integral 4s^2=4s^3/3

    What do I do now, the answer is 16.89 ft. but I dont know how-to get that from the derivation. Need Help Thanks!
  2. jcsd
  3. Feb 2, 2007 #2


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    What've you done here: 1/dt=ads*vdv?

    Your first equation a=4s2 is a differential equation: namely [tex]\frac{d^2s}{dt^2}-4s^2=0[/tex]. Do you know how to solve such an equation?
  4. Feb 2, 2007 #3
    Integral 4s^2=4s^3/3
  5. Feb 2, 2007 #4
    help me solve this please
  6. Feb 2, 2007 #5
    need help i dont know what to do
  7. Feb 2, 2007 #6
    Cristo gave you the equation, so solve the diff eq. Also the answer to the problem that you posted 16.89 ft, is not right. The question isn't asking for a numerical answer.

    Another way is take the equations you have V=ds/dt a=dv/dt and eliminate dt and just integrate and do the algebra.
  8. Feb 2, 2007 #7
    can you post how you did it please
  9. Feb 2, 2007 #8
    if you got 15, for the answer thats not it also
  10. Feb 2, 2007 #9


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    s4orce, the question is not looking for a numerical answer; it is looking for an expression for velocity. The way I would do it, would be to solve the ODE I gave you in post 2, and then differentiate the answer wrt time.

    Do you know how to solve such a differential equation?

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