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henpen Group Title

Power and work \[ W= \int P dt = \int Fv dt= m \int \frac{dv}{dt} vdt=m \int vdv= \frac{1}{2}m(v_1^2-v_0^2) \] Is this true?: -Did I oversimplify somewhere? -Is this unphysical?

  • 2 years ago
  • 2 years ago

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  1. henpen Group Title
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    \[ W= \int\limits P dt = \int\limits Fv dt= m \int\limits \frac{dv}{dt} vdt=m \int\limits vdv= \frac{1}{2}m(v_1^2-v_0^2) \]

    • 2 years ago
  2. Algebraic! Group Title
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    it's fine.

    • 2 years ago
  3. 03225186213 Group Title
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    correct

    • 2 years ago
  4. Kainui Group Title
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    Similarly, \[W=\int\limits_{}^{}Fdx=\int\limits_{}^{}madx=m \int\limits_{}^{} \frac{ dv }{ dt } dx=m \int\limits_{}^{} \frac{ dv }{ dx }\frac{ dx }{ dt } dx = m \int\limits_{}^{} v dv=\frac{ 1 }{ 2 }mv^2\]

    • 2 years ago
  5. henpen Group Title
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    @Kainui That's what I did.

    • 2 years ago
  6. Kainui Group Title
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    No, you did something slightly different. You used power, I did not.

    • 2 years ago
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