The physics
A charge q in a field E feels a force qE. A + charge moves along E. A − charge, like an electron, moves against it.
Two plates a gap d apart sit at a voltage V. The field between them is the same everywhere.
E = V / d F = q E a = q E / m
The field's work on a charge that moves through a voltage V is qV. From rest, it all becomes kinetic energy.
q V = ½ m v² W = q E·Δr
An electron fired across the field keeps its forward speed. The field bends it into a parabola, like a ball thrown sideways.
y = ½ a (L / v)² tan θ = vy / v
A field that changes with time gives a force that changes too. Add the pushes over time: v = ∫ a dt.