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an object's acceleration is given by the function a= 2/v^2, determine an expression for the velocity of the object as a function of time. (at t= 0, v=0)

  • physics -

    dv/dt = 2/v^2
    v^2*dv = 2 dt
    Integrate both sides from t=0, v=0
    v^3/3 = 2 t
    v = [6 t]^1/3

    Check: a = dv/dt = (1/3)*(6 t)^-2/3*6
    = 2*(6t)^-2/3 = a/v^2

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