Question

When electric field is applied in a conductor, it should cause acceleration, why then do the electrons acquire a steady average drift velocity?

Answer 1

When electric field is applied in a conductor it increases the drift velocity of the electrons but on collision of these electrons with the ions of the metal, the electrons lose its drift speed. Again the electric field starts to accelerate and increase its drift velocity and again the electrons suffer collision with the ions of the metal and this process continues and the electrons acquire steady average drift velocity and not the acceleration.