Why?
My particle is moving along z and v=[0,0,v
_{z}]
of course it will have a displacement along x and y but the intial velocity has only one component.
Could you please explain your point?
Quote by tinytim
Where do the 1/v come from?

it comes from the differential equation:
dv
_{x}/dt=qE
_{x}/m
dv
_{y}/dt=qB
_{x}v
_{z}/m
I change the variable t in z... it is a bit of algebra I can write you everything if you want so you can double check my manipulation.