Answer
$v = 4.02\times 10^{-4}~m/s$
Work Step by Step
Let $N$ be the number of electrons per $m^3$
$i(t) = v~A~q~N$
We can find the average velocity $v$ of the electrons.
$v = \frac{i}{A~q~N}$
$v = \frac{i}{\pi~r^2~q~N}$
$v = \frac{15~\sqrt{2}~C/s}{\pi~(1.025\times 10^{-3}~m)^2(1.6\times 10^{-19}~C)(10^{29}~electrons/m^3)}$
$v = 4.02\times 10^{-4}~m/s$