The classical theory of collision induced emission (CIE) from pairs of dissimilar atoms is studied. This radiation emitted by accelerating dipoles is produced essentially by their overlap and exchange interaction at short range. This classical calculation is based on exact collinear solutions of the trajectories of two spherical particles in a head-on collision under the influence of a Morse potential with a well of arbitrary depth. Without too restrictive conditions a variety of simple solutions in closed form is obtained that illustrates the connection between collision dynamics and CIE. Depending on the well depth and energy of the particles, they may radiate in the far infrared to infrared or visible and shorter wavelength regions. The results are characterized by a fixed total energy. Nevertheless, a connection is demonstrated between the line shape in CIE computed through the trajectory and that based on the emission of a thermally equilibrated system.