Question #43934

A conducting rod of mass $m$ and length $l$ rests on two long, parallel, horizontal conducting rails separated by a distance $l$. A uniform vertical magnetic field $B$ exists throughout the region. The rails are connected in series to a DC voltage source $V_0$, a resistor $R$, an inductor $L$, and a switch. The coefficients of static and kinetic friction between the rod and the rails are $\mu_s$ and $\mu_k$, respectively ($\mu_s > \mu_k$). Additionally, when moving, the rod experiences an aerodynamic drag force $F_d = -kv$, where $v$ is its velocity and $k$ is a positive constant. The switch is closed at $t=0$. Assuming $V_0 l B > \mu_s mg R$, the rod eventually starts moving. Let $a_0$ be the acceleration of the rod immediately after it begins to move, and $v_f$ be its steady-state terminal velocity. Which of the following expressions correctly gives the pair $(a_0, v_f)$?