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Constant Power and speed of particle relation

  1. Mar 29, 2005 #1
    Hello all

    I encounter a difficulty solving most simple problem related to constant power and speed of particle the problem is as follows:

    Express the speed (V) of a car given a constant power P , the mass of the car is m, the car travels distance x and it at first was at rest.

    I assume initial speed and dist. is zero, if P is constant I can write it as P=FV so
    V=P/F ; F=mA (where A is acceleration) here I feel there should be some integration but I don't know how to continue ?

    Help will be appreciated! :mad:
     
  2. jcsd
  3. Mar 29, 2005 #2

    dextercioby

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    Why do they give you the distance "x"...?It requires a simple integration.

    [tex]P=m\frac{dv}{dt}v [/tex]

    Do u see how to derive [itex] v(t) [/itex]...?

    Daniel.
     
  4. Mar 29, 2005 #3
    No I'm not so good with diff. equations .!
     
  5. Mar 29, 2005 #4

    dextercioby

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    Separate variables and integrate with corresponding limits...

    [tex] v \ dv =\frac{P}{m} dt [/tex]

    Daniel.
     
  6. Mar 29, 2005 #5
    Already made but the answer is given by x ,p ,m and factoring numbers !
    I think DX/DT is needed ??/
     
  7. Mar 29, 2005 #6

    dextercioby

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    It can't."x" given in the problem is a number.I don't know why they gave it,though...

    Daniel.
     
  8. Mar 29, 2005 #7
    I can post the answer for you it goes like : v=(3xp/m)^(1/3)!!!!
    The question is from Resnick Physics 1 4th edition chapter 7 problem 52 , I suppose the answer is correct .
     
  9. Mar 29, 2005 #8

    dextercioby

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    Okay the velocity is

    [tex] v=\sqrt{\frac{2P}{m}} \sqrt{t} [/tex] (1)

    Integrate wrt time & use the initial condition (t=0,x=0) to find

    [tex] x=\frac{2}{3}\sqrt{\frac{2P}{m}} \ t^{\frac{3}{2}} [/tex] (2)

    Eliminate "t" between (1) & (2) & u'll find your answer.

    Daniel.
     
  10. Mar 30, 2005 #9
    Thank you very much
    I got it , good to know there are wise people out there.
     
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