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Math Help - [SOLVED] Is the runner running continuously?

  1. #1
    Mooch22
    Guest

    [SOLVED] Is the runner running continuously?

    The rate of a runner running the 400 meter run in 50 seconds is given by a differentiable function r(t). The table below shows the rate as measured every 5 seconds.

    Time (Seconds) Rate(m/sec)
    0--------------------0
    5--------------------5
    10-------------------7
    15-------------------10
    20-------------------12
    25-------------------13
    30-------------------11
    35-------------------9
    40-------------------8
    45-------------------7
    50-------------------6

    A.) Explain why r(t) is a continuous function.

    B.) Given some time (t=c) on (0,50) and using correct units, explain the meaning of

    lim ((r(c)-r(t))/(c-t))
    t-->c

    C.) Is there some time on the interval (0,50) such that r'(t)=0? Explain.

    D.) Find the average acceleration on [10,40]. Label the answer in correct units.

    E.) Approximate as accurately as possible the acceleration of the runner at t=30 seconds algebraically.
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  2. #2
    MHF Contributor
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    For part a), pay attention to what info was given to you. What does differentiability imply?

    Jameson
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