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My textbook says

The equation for drift velocity tells us that electrons move with an average velocity which is independent of time although electrons are accelerated.

I have a few questions.

  1. Why is acceleration constant here?
  2. Why is the relaxation time also constant?
  3. How does acceleration of an object and its dependence on time related? Is it v =u + at?
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  1. Why is acceleration constant here?

The acceleration only depends on the applied Electric Field (because of the potential difference created by the battery). Its value would be $\dfrac{charge*Electric Field}{mass}$

  1. Why is the relaxation time also constant?

The relaxation time is just the average value. Collision time is related to kinetic energy so it would depend on the temperature. Hence, constant.

See this for more on relaxation time.

  1. How does acceleration of an object and its dependence on time related? Is it v= u + at?

Average values are used in this equation. The motion of the electrons in the absence of an electric field will be equally distributed in all the directions, making the net value of initial velocity $u = zero$.

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