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Homework Help: Help finding instantaneous velocity graphically

  1. Jan 31, 2012 #1
    A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the instantaneous velocity at the following instants.
    Untitled22.jpg

    (a) t = 1.00 s

    (b) t = 3.00 s

    (c) t = 4.50 s

    (d) t = 7.50 s

    I know that a) is 5 m/s and c) is 0 m/s, but I need help figuring out b) and d). I don't understand how to draw the tangent line to find the instantaneous velocity.

    For 3.00 s the answers I've come up with are wrong. I though using the slope of two points on the line, (7-10)/(3-2) should give me the answer. Any help?
     
    Last edited: Jan 31, 2012
  2. jcsd
  3. Jan 31, 2012 #2

    SammyS

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    Since each of those times corresponds to a position at which the graph is a straight-line segment, and not where two segments meet, the slope of the tangent line is equal to the slope of the line segment.

    You have the right idea with (7-10)/(3-2), it's just that the position at t = 3 s, is a bit in excess of 7 m. Use the whole segment from t = 2s to t = 4 s.
     
  4. Jan 31, 2012 #3
    When the average velocity doesn't change over a certain period of time, the instantaneous velocity is going to be the same.

    It's like trying to find the average grade of five students who all got a 95 on the test
     
  5. Jan 31, 2012 #4
    Thanks so much! I didn't realize I should take the slope of the whole line. I worked them out and they're correct.
     
  6. Jan 31, 2012 #5

    SammyS

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    Good!

    If you use the slope you got and go back to find what x is at t=3s, I think you'll find that x = 7.5m. It's hard to read the graph that accurately.
     
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