K.E. = q2E2t2 / 2m is the formula of columb's law.
Law of Coulomb
The electrostatic force between two charged items is inversely proportional to the square of the distance between the two objects and directly proportional to the product of their charges.
Electrostatic force,
F = q E
m (dv/dt) = q E
Integrating, we will get,
v = q E t / m + c
where c= integraing constant.
at t = 0, v = 0, so c = 0
now, v = q E t / m
Therefore,
K.E. =1/2 m v2
K.E. = q2E2t2 / 2m
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