Why is the average velocity of an electron at time $t$ equal to zero in the absence of an external electric field?

Drift velocity $V_d$ varies with the intensity of electric field $E$ as per the relation:

Drift speed $(v_d)$ varies with the intensity of the electric field $(E)$ as per the relation:

$A$ current $I$ flows through a uniform wire of diameter $d$,when the mean drift velocity is $v_d$. The same current will flow through a wire of diameter $d/2$ made of the same material,if the mean drift velocity of the electrons is

$A$ current of $5\; A$ is passing through a non-linear magnesium wire of cross-section $0.04\; m^2$. At every point,the direction of current density is at an angle of $60^{\circ}$ with the unit vector of the area of cross-section. The magnitude of the electric field at every point of the conductor is .... $V/m$ (Resistivity of magnesium is $\rho = 44 \times 10^{-8}\, \Omega m$).

Find the mobility of an electron in a wire if its average collision time is $9.1 \times 10^{-15} \,s$. (Charge of electron $= 1.6 \times 10^{-19} \,C$ and mass of electron $= 9.1 \times 10^{-31} \,kg$)