The magnatic force on the wire of length d due to magnetic field is `F=IBd sin 90^@=IBd`
This force, according to Left Hand Rule, acts perpendicular to the wire in the plane of paper towards left hand side. Due to it, the wire moves towards left with the acceleration.
`a=F/m=(IBd)/(m)`
Velocity of the wire at a time t will be
`v=u+at=0+(IBd)/(m)t`
or `v=(IBd)/(m)t` towards left