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19 July, 13:02

An object oscillates in the x direction with a position of x (t) = 3cos (2πt), where distance is measured in meters and time is measured in seconds. what is the speed of the object at t=1s?

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  1. 19 July, 13:22
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    For this case we have the following position equation:

    x (t) = 3cos (2πt)

    Deriving to obtain the speed we have:

    x ' (t) = - 3 * 2 * π * sine (2πt)

    Substituting for t = 1 we have:

    x ' (1) = - 3 * 2 * π * sine (2π (1))

    Rewriting:

    x ' (1) = - 6πsine (2π)

    x ' (1) = - 6π (0)

    x ' (1) = 0

    Answer:

    The speed of the object at t = 1s is:

    x ' (1) = 0 m / s
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