Drift Velocity: missing 1/2?

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Main Question or Discussion Point

If a is the acceleration of an electron in a conductor due to an electric field, and t is the mean time between collisions, than v_d, the average drift velocity, is

v_d = at

1. There should be a 1/2 there! If you followed one electron, its average v_d would be at/2 by kinematics.
2. Book says: We're averaging over many electrons. For each one, at some instant, v_d = aT where T is the time since the last collision. And what's the average of that? Just v_d = at.

Which one is right? They both sound correct to me...
 

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