Why do electrons acquire a steady drift velocity? Give reason.

When the electric field is applied across the ends of the resistor, the free electrons of the resistor accelerate and hence gain kinetic energy. These electrons collide with nearby electrons and lose their kinetic energy and the other electrons also accelerate which again collide and hence this process remains continuous. After some time, electrons gain a constant speed opposite to the electric field applied which is called drift velocity.

The drift velocity in the wire is given by I = neAV_d , where n is the number of free electrons per unit volume, e is the electric charge, 'I' be the current flowing and A be the cross-sectional area of the wire.