If the "coil" is just a long conductor, you can use:
e=lvBsinx
Where e is the voltage, l is the length, v is the velocity and B is (sorry, I only know the correct term in Finnish) the magnetic field's density.
If you know more about the coil (for example it's shape), you can calculate the velocity using:
e=-N(ΔΦ/Δt)
Where N is the number of loops in the coil and Φ is the magnetic flux. A (seen below) is the surface area of the cross section of the coil. Let's take for example a rectangular coil with A=l*w, where l is the lenght and w is the width.
e=-N(ΔA*B/Δt)
ΔA/Δt=e/(-N*B)
Δl/Δt=e/(-N*B*w)
There you have the velocity.