The electron beam, passing between the plates of the flat capacitor parallel to them, is displaced by 1 mm. Determine the speed

The electron beam, passing between the plates of the flat capacitor parallel to them, is displaced by 1 mm. Determine the speed of the electrons before entering the capacitor. The length of the plates is 5 cm, the field strength in the capacitor is 15 kV / m.

The electron flies in at an unknown speed Vx, moving parallel to the plates and perpendicular to the field. Vx speed is constant. Under the action of the field, the charge with acceleration a begins to shift against the lines of the field (the charge is negative), because the force F = eE acts on it, where e is the electron charge, E is the field strength.
Let us find the acceleration a from the relation ma = eE:
a = eE / m (1),
where m is the electron mass, e is the electron charge.
Let us determine the time of flight of an electron through a capacitor:
t = S / Vx (2) (S = 5 cm is the length of the plates).
In time t, the electron will be displaced by a distance d = 1 mm:
d = (at ^ 2) / 2.
Answer: The speed of an electron before entering the capacitor is 57 426 258 m / s