Interacting charges and the classical electron radius

The equation of the motion of a point charge $q$ repelled by a fixed point-like charge $Q$ is derived and studied. In solving this problem useful concepts in classical and relativistic kinematics, in Newtonian mechanics and in non-linear ordinary differential equations are revised. The validity of the approximations is discussed from the physical point of view. In particular the classical electron radius emerges naturally from the requirement that the initial distance is large enough for the non relativistic approximation to be valid. The relevance of this topic for undergraduate physics teaching is pointed out.