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Finding Instantaneous Acceleration/Velocity

  1. Nov 11, 2008 #1
    Hi, you guys seem really helpful so I didnt think the template was necessary as my question dosent really fit those guidelines.

    Im currently working on a review sheet for my Physics test tomorrow, and am having trouble finding the instantaneous velocity from looking at a acceleration vs. time graph and the instantaneous velocity from a position vs. time graph.

    the problems i need help with are 1c and 2d on this page:http://www.jburroughs.org/science/mschober/consta/sframe.htm

    Im just looking for a general method on how to complete these problems.

    thanks so much in advance, Adam
     
  2. jcsd
  3. Nov 11, 2008 #2

    djeitnstine

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    using an acceleration vs. time graph you simply need to find the tangent at that point. remember [tex]Lim _{\Delta x \rightarrow 0}[/tex] [tex]\frac{f(x+\Delta x)-f(x)}{\Delta x}[/tex]

    And for velocity from a position vs. time graph you just need to find the area under the graph. [tex]\sum f(x) \Delta x[/tex]
     
  4. Nov 11, 2008 #3
    thanks for the reply, but Im still kind of confused. When looking at a position vs. time graph, wouldnt the area under the curve be the velocity over that time interval, not the specific time?
     
  5. Nov 11, 2008 #4

    djeitnstine

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    Oops I have all of that backwards.

    let me rewrite that:

    using a position vs. time graph you simply need to find the tangent at that point. remember [tex]Lim _{\Delta x \rightarrow 0}[/tex] [tex]\frac{f(x+\Delta x)-f(x)}{\Delta x}[/tex]

    And for velocity from a acceleration vs. time graph you just need to find the area under the graph. [tex]\sum f(x) \Delta x[/tex]

    I'm really sorry if I confused you.
     
  6. Nov 11, 2008 #5
    ok gotcha. Just curious, is there any other simpler way to find the inst. velocity that finding the tangent? It takes a long time and seems to be pretty inaccurate.
     
  7. Nov 11, 2008 #6

    djeitnstine

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    Just take the derivative of the function at hand for the position/time graph and take the integral of the acceleration/time graph (derived using the formulas I gave you above.)
     
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