Answer
See explanation.
Work Step by Step
$$\epsilon = vBL$$
Consider the units of the right hand side of this equation. The units of tesla are a newton per amp-meter.
$$\frac{m}{s}\frac{N}{A\cdot m}m$$
An ampere is a coulomb per second.
$$\frac{m}{s}\frac{N \cdot s}{C\cdot m}m$$
$$\frac{N \cdot m}{C }$$
A newton-meter is a joule.
$$\frac{J}{C }$$
A joule per coulomb is a volt, which are the units of emf.