(i) When conductor is subjected to an electric field E, each electron experience a Force.

F=−eE
and acquires an acceleration
a=‌

F

m

=−‌

eE

m

.......(i)
Here m= mass of electron, e= charge,
E=‌ electric field. ‌
The average time difference between two consecutive collisions is known as relaxation time of electron.

τ=‌

τ1+τ2+−−+τn

n

......(ii)
As v=u+at (from equations of motion.)
The drift velocity vd is defined as -
vd=‌

v1+v2+⋯+vn

n

vd‌=0+‌

a(τ1+τ2+⋯+τn)

n

(average thermal velocity =0)
∴‌‌vd‌=0+aτ
vd‌=−(‌

eE

m

)τ‌‌ [from (i)] ‌
(ii) According to drift velocity expression, relaxation time is the time interval between successive collisions of an electron on increasing temperature, the electrons move faster and more collisions occur quickly. Hence, relaxation time decreases with increase in temperature which implies that drift velocity also decreases with temperature.