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Very trick velocity vs. time graph

  1. Mar 17, 2009 #1
    Very tricky velocity vs. time graph

    1. The problem statement, all variables and given/known data
    Doing a very basic lab on force and motion and ran into a snag with a graph. It's a very wildly changing acceleration graph, and I'm unsure how to proceed with the matching velocity graph. I know that a curved acceleration graph would indicate an even more steeply curved velocity graph, but I'm mentally visualizing too many positive and negative accelerations to get my head around this. Please help.

    2. Relevant equations

    http://usera.imagecave.com/hotrod73dart/question/Vgraph.jpg

    3. The attempt at a solution

    http://usera.imagecave.com/hotrod73dart/question/vgraphattempt1.jpg
     
    Last edited: Mar 17, 2009
  2. jcsd
  3. Mar 17, 2009 #2
    Have you taken a calculus class yet? If you have not those sharp points in your velocity graph (i.e. at t = 1) do not have continuous derivatives, so that cannot be the answer because, well, you have the acceleration graph which is continuous.

    Remember that a = dv/dt so it's the change in the velocity. So where ever the acceleration is positive the velocity will be increasing, does this help at all?
     
  4. Mar 17, 2009 #3
    No calculus yet unfortunately. Those sharp points are supposed to be sharply rounded curves, but I don't think that makes much sense either. I'm aware of what acceleration is, but when acceleration is changing at a non-constant rate (curved acceleration graph), then that means that velocity is increasingly increasingly increasing (or increasingly increasingly decreasing). Not an easy thing to visualize. Add positive and negative acceleration and positive and negative velocity into the mix and it gets really confusing.
     
    Last edited: Mar 17, 2009
  5. Mar 17, 2009 #4
    Maybe this will help: http://filer.case.edu/pal25/pic.jpg [Broken]

    You're right it is hard to visualize the first time you see it, but it gets easier the more you analyze these graphs.
     
    Last edited by a moderator: May 4, 2017
  6. Mar 17, 2009 #5
    Re: Very tricky velocity vs. time graph

    If my newest attempt is correct then yes, your image helped very much. Otherwise, I'm still lost.

    http://usera.imagecave.com/hotrod73dart/question/vgraphattempt3.jpg
     
    Last edited by a moderator: May 4, 2017
  7. Mar 17, 2009 #6
    Yes, that looks right.
     
  8. Mar 17, 2009 #7
    Looks good....the only thing is that the final velocity might not be that high.

    As Feldoh said, it's hard to visualize, but the more experience you get, the easier it gets.
     
  9. Mar 17, 2009 #8
    Thanks so much. It was very difficult until Feldoh pointed out the fact that while the acceleration graph was sloping downward it was still a positive value, meaning that velocity was still increasing, just not as largely incremental. Then it was easy to extrapolate that the negative acceleration merely negated the initial positive acceleration and brought the velocity back to the original value.

    I love physics, but sometimes I feel it's going to be the death of me (and this is only 100 level!)
     
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