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Can anyone explain this integration for me?

  1. May 15, 2017 #1
    1. The problem statement, all variables and given/known data
    http://imgur.com/a/Y8NW0

    Basically we start with a function of t, which was differentiated twice, that function = [itex] F_o / m [/itex]

    Fo is a constant force, and I assume m is mass though my book doesn't state that.

    2. Relevant equations


    3. The attempt at a solution

    Integrating the function, I multiply m to the other side, because I assume m is mass and mass is a constant. so it shouldn't really matter.

    since F_o is a force, that means it is Kg * m/s^2, divided by mass which is in kg, you get m/s^2 which is indeed acceleration, the second derivative of time.

    Integrating, I get

    [itex] m\int x^{''}(t) \, dt = \int F_o \, dt [/itex]

    [itex] m\int x^{''}(t) \, dt = F_o(t) [/itex]

    But as you see from the link I provided, the book states
    [itex] m\int x^{''}(t) \, dt = F_o(t) + V_o[/itex]

    First off, I don't even know what V_o is. Is it inital velocity, or is it final velocity? It would make sense for it to be final velocity since [itex] m\int x^{''}(t) \, dt [/itex] is literally velocity itself..

    I was under the impression that if you integrate something with respect to time, and that function does not have a time variable, it would simply be that function times the variable t.

    Why is it that they are adding V_o in this example?
     
  2. jcsd
  3. May 15, 2017 #2
    I marked it as solved. I guess I didn't read clearly enough, V_o is the constant of integration.

    That makes sense now. Always end your integrals with + C, I feel dumb now..
     
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