Electric Charges and Fields

EXPLANATION Force on the charged particle:When a particle of charge $q$ is placed in a uniform electric field $\vec{E} = E_0 \hat{i}$, the electrostatic force acting on it is given by:$$F = q E_0$$Acceleration of the particle:Using Newton's second law ($F = ma$), the acceleration $a$ of the particle of mass $m$ is:$$a = \frac{F}{m} = \frac{q E_0}{m}$$Kinetic Energy calculation:Since the particle starts from rest ($u = 0$) and travels a distance $x$, we can use the third equation of motion ($v^2 = u^2 + 2ax$):$$v^2 = 0 + 2 \left(\frac{q E_0}{m}\right) x = \frac{2 q E_0 x}{m}$$Now, substitute $v^2$ into the formula for Kinetic Energy ($K = \frac{1}{2} m v^2$):$$K = \frac{1}{2} m \left(\frac{2 q E_0 x}{m}\right) = q E_0 x$$