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Math Help - Velocity/displacement problem

  1. #1
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    Velocity/displacement problem

    Hello,

    I am not very good at calculus to begin with, especially word problems and velocity problems. I have no idea how to start this one out, so if someone could show me how, that would be great to give me a start. Here goes:

    The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 5sin(πt) + 2cos(πt), where t is measured in seconds. (Round all answers to the nearest hundredth.)

    there are multiple sub-questions, but I'll just give two:

    (a) Find the average velocity during the time period [1, 2] (in cm/s).
    (e) Estimate the instantaneous velocity of the particle when t = 1 (in cm/s).

    I haven't the slightest clue other than I'm (guessing) it has something to do with Galileo's law, s(t) = 4.9t^2,but I have no clue where/when I should apply it or in addition to another formula.

    Any help would be awesome! Thanks.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    No this has nothing to do with Galileo's Law it is a completely different
    motion problem.

    What stays the same is the definition of average velocity it is still

    [s(t2) - s(t1)]/(t2-t1)

    s = 5sin(πt) + 2cos(πt

    Compute [s(2) -s(1)]/[2-1]

    The instantaneous velocity is the derivative but as you've been asked for
    an approximation I'm assuming you haven't done derivatives yet?

    Compute [s(1.01) -s(1)]/[1.01-1]
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  3. #3
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    No, we haven't done derivatives yet, those are in the next unit. I was just thinking it may have something to do with Galileo's Law because the question previous had it and the beginning of the section explains it. I will give it a try, thanks for the help
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