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1.3 Iridov - Find Time Interval ( Kinematics )

  1. Apr 10, 2009 #1
    Thank you for taking the time to read this lengthy post.

    A car starts moving rectilinearly, first with acceleration a=5m/s2(the initial velocity is 0) then uniformly, and finally, decelerating at the same rate a, comes to stop.The total time of motion equals 25 seconds. The average velocity during whole time is 72 km/h. How long does the car move uniformly?


    http://img26.imageshack.us/img26/1403/defaultx.png" [Broken]

    All my equations appear to be correct; however, when I calculate the t_{o}, I get an imaginary answer. What did I miss or do wrong?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 10, 2009 #2


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    Maybe consider the area of a trapezoid?

    That is what your V(t) graph represents.

    You know that the integral of V(t) yields X(t)

    They tell you what the area is ... avg V * total T = 20 * 25 = 500.

    The base is 25 sec and total X is 500
    So ...

    (25+X)/2*H = 500

    You also know that X = 25 - 2d
    where d is the 2 periods of acceleration and deceleration.

    And H = 5*d
    where V = 5*t so ...

    H = 5*(25 -X)/2

    Combining things then yields:

    5*(25 -X)/2*(25+X)/2 = 500

    5/4*(252 - X2) = 500

    I get a real result.
  4. Apr 10, 2009 #3
    Actually, I ignored the graph I drew when I solved the problem because I realized(on another piece of paper) that the area I was calculating (two triangles and rectangle) was identical to D = 2x_o + x_1.

    This may be asking too much but can you find the mistake in my work? I just don't see it.

    Thanks again.
  5. Apr 10, 2009 #4


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    Now that you know the answer, you can work backwards to figure the error in your math. In all honesty, I'm not that interested in looking.
  6. Apr 11, 2009 #5


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    Gold Member

    EDIT : My mistake.
    Last edited: Apr 11, 2009
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