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Math Help - Integrating a graph problem

  1. #1
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    Integrating a graph problem

    A car is traveling on a straight road. For 0 =< t =< 24 seconds, the cars velocity v(t), in meters per second, is modeled by the piecewise-linear function defined by the graph below.

    a.) Find \int_0^{24} v(t) dt. Using correct units, explain the meaning of \int_0^{24} v(t) dt.

    b.) For each of v'(4) and v'(20), find the value or explain why it does not exist. Indicate units of measure.

    c.) Let a(t) be the cars acceleration at time t, in meters per second per second. For 0 < t < 24, write a piecewise-defined function for a(t).

    d.) Find the average rate of change of v over the interval 8 =< t =< 20. Does the mean value theorem guarentee a value of c, for 8 < c < 20, such that v'(c) is equal to the average rate of change. Why or why not?


    For a.) I came up with the answer 360 meters, I'm pretty sure that is correct.
    For b.), I think the acceleration would be zero, correct me if I'm wrong.
    I don't know what to do for c.) and d.) any help is appreciated, thanks.
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  2. #2
    MHF Contributor chisigma's Avatar
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    The quantity...

    \displaystyle \int_{0}^{24} v(t)\ dt (1)

    ... is simply the area of the 'trapetium' of the figure and it can be computed with a simple geometric approach...

    Kind regards

    \chi \sigma
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  3. #3
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    Thanks for the reply, as I said I figured out the area, but I could use some help on the other questions. Thanks for your time.
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  4. #4
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    Sorry for the double post, but could anyone help me with c and d, thanks.
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