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Dot product of v and v'

  1. Mar 10, 2015 #1
    In a book I was reading, it says
    F=mv'=P'

    so dot producting on both sides with v

    Fv = mv ⋅ dv/dt = 1/2 m d(v2)/dt = d(1/2 m v^2)/dt


    I really don't get how v ⋅ dv/dt = 1/2 d(v2)/dt.
    I have seen few threads and they say it's about product rule, but they don't really explain in detail.

    Could anyone help me with this?
     
  2. jcsd
  3. Mar 10, 2015 #2

    PeroK

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    Science Advisor
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    Gold Member

    Welcome to PF!

    ##v^2 = \textbf{v.v}##

    Can you now differentiate that equation?
     
  4. Mar 10, 2015 #3

    jedishrfu

    Staff: Mentor

    V^2 = V . V

    And the time derivative of it is V' . V + V . V'
     
  5. Mar 10, 2015 #4


    Oh.. I see. I did not now that d(x ⋅ y)/dt = x' ⋅ y + x ⋅ y'

    Knowing this, going right from left is easy, but I guess going left to right needs some practice to spot!

    Thank you both peroK and Jedishrfu!
     
  6. Mar 10, 2015 #5
    In Cartesian component form, what is ##\vec{v}\centerdot d\vec{v}##?

    Chet
     
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