Please Help with Electron Moving to make Electric Field?

Use the force on the electron by a an electric field strrength of E:

F = qE = ma

Now you know the initial, v0, and final. vf, speeds and the distance, x, it moved between those speeds, so you can find acceleration,a from

x = (vf^2 -v0^2)/(2a) ---> a = (vf^2 -v0^2)/(2x)

So the field strength is

E = (m/q) (vf^2 -v0^2)/(2x) where q = -1.6x10^-19 Coul and m = 9.11x10^-31 kg

Recall that,

E = F / q

F = ma

a = (change in velocity) / (time taken for the change)

To find the time we use the equation of motion which says that,

Distance = (change in velocity / 2) * t

t = 2 * distance /( change in velocity) = 2 * x / ∆v

Putting all this together we have

E = m * ∆v / q t = m * ∆v * ∆v / q ( 2 * x)

so,

∆v = (6.36 - 3.18) * E +7 = 3.18 * E +7 m/s

x = 0.0474 m

m = 9.109 × E -31 kg

q = - 1.6 E - 19 C

If we find just the magnitude of the E-field, we can ignore the minus sign of the electron charge.

E = (9.109 × E + -31 ) * (3.18 * E +7)^2 / (1.6 E - 19 ) * (2 * 0.0474 )

E = 6073 * E + 2 = 607300 = 6.073 E +5 N/C