A conducting bar of mass \(m\), length \(\ell\), and electrical resistance \(R\) rests on two long, horizontal, frictionless conducting rails of negligible resistance located in a uniform, vertical magnetic field of magnitude \(B\). The rails are connected at one end by a wire of negligible resistance to form a closed circuit. As the bar moves, it experiences an ambient fluid drag force \(\vec{F}_{\text{drag}} = -b\vec{v}\), where \(b\) is a positive constant and \(\vec{v}\) is the velocity of the bar. At time \(t = 0\), the bar is launched along the rails with an initial speed \(v_0\). Which of the following expressions correctly represents the speed \(v(t)\) of the bar as a function of time \(t\)?