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Instantaneous velocity

  1. Jul 4, 2005 #1
    hi all having a problem with this question:

    The position of a rabbit along a straight tunnel as a function of time is plotted: [​IMG]
    1. What is its instantaneous velocity at t = 10.0s and t=30.0s
    2. what is the average velocity:
    between t = 0 and t = 5.0s
    between t = 25.0s and t = 30.0s
    between t = 40.0s and t = 50.0s

    i can do it when they give an equation. and i know it has to all do with tangents and all that, i can get the results by "estimating", but not as accurate. im totally stuck with this one any help at all will be appreciated.

  2. jcsd
  3. Jul 4, 2005 #2


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  4. Jul 4, 2005 #3
    Instantaneous means the derivative at that point in time; average is the slope formed between the points.
  5. Jul 4, 2005 #4
    yeh i know that but how do you get the equation? i understand taking 2 points eg. (x1,y1)(x2,y2) but i cant find a reliable way of finding them
  6. Jul 4, 2005 #5
    this problem is to determine instant velocity GRAPHICALLY.
    you don't need any "equations" in the usual sense.
    instant velocity is the SLOPE of the tangent line at a point along the curve.
    just determine the slope of the tangent line using (Δx/Δt) by choosing 2 points along the tangent line (1 point can be that at which the tangent line is tangent to the curve) and calculate (Δx/Δt)=(x2 - x1)/(t2 - t1). see this diagram:
  7. Jul 4, 2005 #6


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    Apparently the tangent lines are already drawn on the graph at t= 10 and 30. For the tangent line at t= 30, it appears to me that the line crosses y= 0 around x= 18 and crosses y= 25 around x= 36. The slope of the tangent line is 25/(36-18)= 25/18 or about 1.39 and that is the instantaneous speed at t= 30. That's about the best you can do given that information.
  8. Jul 5, 2005 #7
    you serious? thats what i did exactley but they have answers to 2 decimal places and i kept getting 0.01-0.10 off the answer and i was stressing sooo much i was 90% certain that there must have been a formula.
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