A current flows through a metal rod of length l and mass m  that slides on a frictionless rails as  shown. If initial speed of the rod is  $V_0$ and a magnetic field B  acts out of the plane, then

Magnetic field  $F=Bil$ acts in direction opposite  to motion.
Hence retardation $=\frac{Bil}{m}$ 
So, velocity of rod of time t is 
$V=V_0-\frac{Bil}{m}t$ 
Hence choice (b) and choice (a) is wrong.
From work-energy theorem.
$\frac{1}{2}m{v}_0^2$  = F.S =  $BilS$
or   $S=\frac{m{v}_0^2}{2Bil}$