A conducting rod of mass \(m\) and negligible electrical resistance is free to slide along a pair of horizontal, frictionless, parallel conducting rails separated by a distance \(\ell\). The rails are connected at one end by a fixed resistor of resistance \(R\), and a uniform magnetic field of magnitude \(B\) is directed perpendicular to the plane of the rails. At time \(t = 0\), the rod is moving away from the resistor with speed \(v_0\) while a constant external force of magnitude \(F_0\) is applied to the rod in the direction of its motion, where \(F_0 < \dfrac{B^2 \ell^2 v_0}{R}\). Which of the following best describes the shape of the rod's velocity \(v\) as a function of time \(t\) for \(t \ge 0\)?