The electron drift arises due to the force experienced by electrons in the electric field Inside the conductor. But force should cause acceleration. Why then do the electrons acquire a steady average drift speed ?

Explanation

In a current carrying conductor, each free electron is accelerated instantaneously by acceleration a = `(eE)/(m)` which increases the m drift speed of free electron until it collides with randomly oscillating positive ion in the metal. After collision, free electron comes to rest Again it gets accelerated, again its drift speed increases, again it undergoes another collision, again it comes to rest and so on. Here frequency of such collision is very large and so time lapsed between two successive collisions (known as relaxation time) is very small. Hence, on average we can consider all the free electrons drifting continuously.