Why is the increase in kinetic energy of the particle after being accelerated

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Homework Statement

what is the increase in kinetic energy of the particle after being accelerated by a potential V/2?

The Attempt at a Solution

The textbook says it is q*V/2 but I just wondered why this is the case

 

[Delphi51]

You probably have two defining formulas for electric potential:
1) potential is the energy per charge, V = Ee/q or Ee = qV
This is the very formula you want explained . . . but it is a definition rather than an explanation.

2) Electric potential causes an electric field between electrodes, E = V/d where d is the distance between the plates. The electric force is F = qE so putting E = F/q into the first formula you have F/q = V/d or F*d = q*V. F*d is the work done as the charge moves through the potential difference so W = q*V. Work done is the energy gained so we have energy = qV.