calculus

Find the position function s(t) given acceleration a(t)=3t if v(2)=0 and s(2)=1.

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  1. a(t) = 3t
    v(t) = (3/2)t^2 + c
    v(2) = 0 ----> 0 = (3/2)(4) + c
    0 = 6 + c
    c = -6
    v(t) = (3/2)t^2 - 6
    s(t) = (1/2)t^3 - 6t + k
    s(2) = 1 -----> 1 = 4 - 12 + k
    k = 9

    s(t) = (1/2)t^3 - 6t + 9

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