Answer
$1.87 \times 10 ^{7} m/s$
Work Step by Step
By the conservation of energy,
Loss in energy = Gain in energy
Thus:
$q \Delta V=\frac{1}{2}m_{e}v_{e}^{2}$
$v_{e}=[\frac{2q\Delta V}{m_{e}}]^{1/2}$
$v_{e}=[\frac{2\times 1.6 \times 10^{-19} \times 10^{3}}{9.11\times 10^{-31}}]^{1/2}= 1.87 \times 10 ^{7} m/s$