Calculation and Formula of Drift Velocity

I have seen different textbooks on drift velocity and the derivation of its formula $v = eET/m$ [$e$ - charge of electron, E - external field T - mean time between collisions and m is mass of electron] Though the derivation is the same, using kinematics to get v = u + at and getting acceleration by the force being $eE$ and mass $m$. Some textbooks show the formula as $v = (at)/2$ and some as $v = at$. How? In which case do we use which formula?