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A winding drum raises a cage through a height of 63.0 m. The cage has, at first, an acceleration of 12.0 m/s2 until the velocity of 15.0 m/s is reached, after which the velocity is constant until the cage nears the top, when the final retardation is 5.0 m/s2. Find the time taken for the cage to reach the top in second.

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  1. stage 1:
    a = 12
    v = 0 + 12 t
    h = 0 + 0 t + 6 t^2
    so
    15 = 0 + 12 t
    t = 15/12 = 5/4
    h = 0 + 0 * 5/4 + 6 (25/16) = 9.375 meters
    --------------------------------
    Stage 2:
    a = 0
    v = 15 + 0 t = 15
    h = 9.375 + 15 t + 0 = 9.375 + 15 t where t is time in stage 2
    ---------------------------------
    stage 3
    a = - 5.0 m/s^2
    v = 15 - 5 tt where tt isttime in stage 3
    0 = 15 - 5 tt
    so tt = 3 seconds to stop
    63= (9.375 + 15 t) + 15 tt - (1/2)5 tt^2
    63 = 9.375 + 15 t + 45 - (5/2)9
    63 = 9.375 + 15 t + 22.5
    t = 2.075 seconds at 15
    so add 5/4 + 2.075 + 3 for total time

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