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Acceleration - Displacement Graph

  1. Jul 3, 2014 #1
    In terms of calculus, How do i prove that the area under the acceleration time graph gives me the change in KE / mass.....

    Attempt at solution....

    Area under the graph of a function y = f(x) is given by ∫y dx

    Therefore area under acceleration displacement graph is ∫a ds (considering the function to be a=f(s))

    => ∫f/m ds

    => 1/m (∫f.ds)

    => 1/m (W) .........[work done = ∫f.ds ]

    => ΔKE/m ........[W = ΔKE]


    1. Is this proof correct mathematically and theoretically....
    2. Is there a different or better proof...
     
  2. jcsd
  3. Jul 4, 2014 #2

    SteamKing

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    It's not clear what you are trying to do. First, you talk about the area under the acceleration-time graph, then you talk about the area under the acceleration-displacement graph.

    This is why PF has a HW template and we ask all HW posters to fill out the template when asking a question. It reduces the amount of confusion, which is always lurking to pounce on the unwary.

    https://www.physicsforums.com/showpost.php?p=3977513&postcount=2

    Be sure to include the complete text of the original problem as stated.
     
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