calculus

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Suppose that the velocity of a falling body is v = k/s (k a constant) at the instant the body has fallen s meters from its starting point. Find the body's acceleration as a function of s.

  • calculus -

    v = Vi + a t = 0 + a t
    = a t = k/s
    so
    t = k/(a s)

    s = 0 + . 5 a t^2
    = .5 a t^2

    s = .5 a k^2/(a^2 s^2)
    s^3 a = .5 k^2
    a = .5 k^2/s^3

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