A particle of mass m and charge q is moving in a region where uniform electric field `underset(E)to` and and uniform mag-netic field `underset(B)to`are present. It is given that `underset(E)to/|vec(E)|=underset(B)to/|vec(B)|.` At time t = 0, velocity of the particle is `underset(V)to_(0)` and `underset(V)to_(0).underset(E)to=0.` Write the velocity of the particle at time t.

Answer

`vec(V)cos((qBt)/(m))vec(V)_(0)+((qt)/(m))(vec(E))+sin((qBt)/(m))((vecV_(0)xxvec(B))/(B))`