) An electron of mass m and charge q = -e is released with an initial speed v ; from the center of the hole (at the origin) in the upward direction (along the perpendicular axis [0 the washer) experiencing no forces except repulsion by the charges on the washer. What speed does it ultimately obtain when it is very far away froro the washer (i.e. at infinity)

it depends on the potenial on the washer (or the total charges).

Electron initial KE=1/2 m v^2
electron initial PE=qV

final PE=0
final KE= total initial energy.