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Vf^2 = vi^2 +2ad

  1. Aug 17, 2014 #1
    1. The problem statement, all variables and given/known data

    Can you prove that vf2 = vi2 + 2aΔd?

    2. Relevant equations



    3. The attempt at a solution

    I don't know where to start. I've not been given any values to use so I'm not sure how to go about answering the question.
     
    Last edited by a moderator: Aug 26, 2014
  2. jcsd
  3. Aug 17, 2014 #2

    mfb

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    Staff: Mentor

    What did your course cover so far?
    This is just an application of energy conservation, but I don't know what you can use in such a proof.
     
  4. Aug 17, 2014 #3
    This lesson is about acceleration. It's covered vectors and vector components, relative velocity and displacement so far.
     
  5. Aug 17, 2014 #4
    If you know any of the other kinematic equations then write them down and think about how you can eliminate time as a variable. are there any combinations or substitutions you can make given any of the other kinematic equations?
     
  6. Aug 24, 2014 #5
    Maybe it'll help if I post the entire problem:

    Derive an equation that relates vi, vf, Δd, and a. (Hint: Notice that Δt is not invloved.) Solve for Δt in the first equation. Substitute that value into Δt in the third equation. Solve for vf2. Can you prove that vf2 = vi2 + 2aΔd?

    I think that this equation relates all of the variables that the problem is asking for:

    vf = [itex]\sqrt[]{}[/itex]{vi2 + 2a X d}

    There is a table on the page that the problem doesn't reference specifically but I'm now realizing that it must be relevant:

    DSC_0343.jpg

    solve for Δt for the first equation:

    Δt = (vf - vi) X a

    Substitute that value into Δt for the third equation:
    Δd = ((vi - vf)/2) X ((vf - vi) X a)

    Solve for vf2:
    vf2 = vi2 + 2a X d

    I'm not sure if I did all of that correctly but it leaves me with the initial problem of proving that that vf2 = vi2 + 2aΔd

    I'm not sure I understand where to start with that.
     
  7. Aug 24, 2014 #6
    What do you mean you still have to prove it? you started with true relations and ended up with the required equation; that's how this equation comes about. That's all you need to do.
     
  8. Aug 24, 2014 #7
    My answer should then be yes I can prove that equation because..... ?

    Like I said, I'm not sure I understand where to start with that.
     
  9. Aug 24, 2014 #8
    what you did is proof enough. In this sense derivation would be proof, because like I said, you are taking relations that are already known to be true, and ending up with the time independent kinematic equation.
     
  10. Aug 25, 2014 #9
    I really do appreciate your input. I am pretty stunned when it comes to this stuff.....

    I just don't understand how what I've done above is enough because as you can see here: DSC_0361.jpg

    Proving that equation is the last problem. I have no idea how to answer it.
     
  11. Aug 25, 2014 #10
    Rewrite the equation as ##v_f^2-v_i^2=(v_f+v_i)(v_f-v_i)=2aΔd##

    How is ##(v_f-v_i)## related to a and Δt?

    How is ##(v_f+v_i)## related to the average velocity?

    How is Δd related to the average velocity and Δt?

    Chet
     
  12. Aug 26, 2014 #11
    Could this really be considered a proof? One could easily derive this relation through this method as well.
     
  13. Aug 26, 2014 #12
    Who knows what they were thinking when they asked for a proof?????

    Chet
     
  14. Sep 12, 2014 #13
    lol thanks for your help guys!
     
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