An object of mass \( m \) falling near Earth's surface experiences a resistive force of \( F_{R}=-b v^{2} \), where \( b \) is a positive constant with units of \( \mathrm{N} \cdot \mathrm{s}^{2} / \mathrm{m}^{2} \) and \( v \) is in \( \mathrm{m} / \mathrm{s} \). What is the magnitude of the acceleration of the object when it is moving downward at a speed \( v=\sqrt{\frac{3 m g}{4 b}} \) ?
(A) \( \frac{1}{4} g \)
(B) \( \frac{3}{4} g \)
(C) \( g \)
(D) \( \frac{5}{4} g \)