(Originais Teachy 2023) - Question Very Hard of Physics

A particle of charge q = 2.0×10^-6 C is placed at rest at position A, which is 4.0 cm away from a small positively charged conducting sphere with charge Q = 1.6×10^-6 C. The particle then moves, due to the electric force between it and the sphere, to position B, which is 2.0 cm away from the sphere. Disregard interactions with other charges. Considering the electric potential energy as U = k|qQ|/r, where k is the electrostatic constant of the medium in which the charges are immersed, and r is the distance between the charges: a) Calculate the electric potential energy of the charge-sphere system at position A. b) Determine the work done by the electric force to move the particle from position A to position B. c) Based on energy conservation, calculate the velocity of the particle when it reaches position B. Consider k = 9.0×10^9 N.m^2/C^2.