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The velocity of an object fired directly upwards given v=96-48t, where t is in seconds. When will the velocity be between 48 and 80 feet per second

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  1. 21 June, 13:15
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    The velocity function is

    v (t) = 96 - 48t

    where v is in ft/s

    t is in seconds.

    When v = 48 ft/s, obtain

    96 - 48t = 48

    48 = 48t

    t = 1

    When v = 80 ft/s, obtain

    96 - 48t = 80

    -48t = - 16

    t = 1/3

    The velocity is between 48 and 80 ft/s when t is between 1 and 1/3 seconds.

    The velocity of 80 ft/s is attained first at 1/3 seconds, and the velocity of 48 ft/s is attained later at 1 second.

    The graph illustrates the answer.

    Answer: Between 1/3 and 1 second.
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