Question

A particle with charge \(Q\) and mass \(M\) has instantaneous speed \(u_1\) when it is at a position where the electric potential is \(V_1\). At a later time, the particle has moved a distance \(R\) away to a position where the electric potential is \(V_2\). Which of the following equations can be used to find the speed \(u_2\) of the particle at the new position?

(A) \(\frac{1}{2} M\left(u_2^2-u_1^2\right)=Q\left(V_1-V_2\right)\)

(B) \(\frac{1}{2} M\left(u_2-u_1\right)^2=Q\left(V_1-V_2\right)\)

(C) \(\frac{1}{2} M u_2^2=Q V_1\)

(D) \(\frac{1}{2} M u_2^2=\frac{1}{4 \pi \varepsilon_0} \frac{Q^2}{R}\)</