A broad class of forces P is identified for which the Abraham-Lorentz-Dirac (ALD) equation has common solutions with a Newton type equation that do not present pre-acceleration or escape into infinity (runaway behavior). It is argued that the given class can approximate with arbitrary precision any continuous or piecewise continuous force. For the general case of such forces, the existence of common solutions to the ALD and the Newton type equations in terms of generalized functions defined on P is argued. The existence of such solutions is explicitly demonstrated here for the important example of the instantly connected constant force. Expressions for the position and velocity are defined by generalized functions with point support in the initial time in which force is applied. It follows that both, the velocity as the coordinates are discontinuous at the support point, at the instant where the force is applied. The unusual discontinuity in the position that appears is justified by the presence of impulsive forces that determine instantaneous jumps in the coordinates. This result is compatible with the non relativistic limit under consideration and is expected to be explained after a further relativistic generalization of the discussion here. The solution obtained for this class of forces reproduces the one obtained by A. Yaghjian, from his equations for the extended particle moving between the plates of a capacitor. This outcome suggests the possible link or equivalence between this two analysis. The common solution of the Newton like equations and the ALD ones for the case of a constant and homogeneous magnetic field is also presented. The extension the results to a relativistic limit will be investigated in future works.
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