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Math Help - Average of a function.

  1. #1
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    Average of a function.

    The height at time t of a small weight oscillating at the end of a spring is .5cos(8t).

    How can I find the average velocity over the time intervals [3,4], [3,3.5], [3,3.1]?

    How can i find the weights instantaneous velocity at time t = 3?
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  2. #2
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    Quote Originally Posted by colerelm1 View Post
    The height at time t of a small weight oscillating at the end of a spring is .5cos(8t).

    How can I find the average velocity over the time intervals [3,4], [3,3.5], [3,3.1]?

    How can i find the weights instantaneous velocity at time t = 3?
    You're expected to know and apply the following:

    The average rate of change of a function f(x) over the interval [a, b] is given by \displaystyle \frac{f(b) - f(a)}{b - a}

    The instantaneous rate of change of a function at x = a is f'(a) where f'(x) is the derivative of the function.
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  3. #3
    Senior Member abhishekkgp's Avatar
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    avg velocity = displacement/time taken.
    so over the interval [3,4] avg velocity = (0.5cos(8*4)-0.5cos(8*3))/(4-3). rest can be done in the same way.

    for instantaneous velocity just differentiate the function 0.5cos(8t). put t=3 in the derived function.
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