calculus

a particle moves according to the law a=1/t √t. if s=8 when t=1. and s=16 when t=4. find v when t=9.

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  1. do we have a = 1/(t√t) or is it a = (1/t)√t ??

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  2. a = 1/(t√t)

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  3. ok, then
    a = t^(-3/2)
    v = -2 t^(-1/2) + c

    s = -4 t^(1/2) + ct + k

    case1: s=8, when t = 1
    8 = -4 + c + k
    12 = c + k

    case2: s = 16, when t = 4
    16 = -4(2) + 4c + k
    24 = 4c + k

    subtract them:
    12 = 3c
    c = 4

    back in 12 = c+k
    12 = 4+k
    k = 8

    then v = -2/√t + 4
    when t = 9
    v = -2/3 + 4 = 10/3

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  4. Thank you very, very much. I'm really grateful.

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  5. welcome,

    hope you checked my arithmetic

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