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An apple is dropped from rest. Its vertical velocity \(v(t)\) is governed by the first-order differential equation:$$\frac{dv}{dt} = -g$$where \(g\) is the constant gravitational acceleration. At \(t=0\), the velocity is \(v(0) = 0\).
  1. Determine the general expression for the velocity \(v(t)\) by finding the antiderivatives of the constant function \(-g\).
  2. Using the initial condition \(v(0) = 0\), find the unique velocity function.

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