Post-starburst galaxies host a population of early-type stars (A or F), but simultaneously lack indicators of ongoing star formation such as OII emission. Two distinct stellar populations have been identified in these systems: a young post-starburst population superimposed on an older host population. We present a study of nine post-starburst galaxies with the following objectives: 1) to investigate if and how kinematical differences between the young and old populations of stars can be measured; and 2) to gain insight into the formation mechanism of the young population in these systems. We fit high signal-to-noise spectra with two independent populations in distinct spectral regions: the Balmer region, the MgIb region, and the Ca Triplet when available. We show that the kinematics of the two populations largely track one another if measured in the Balmer region with high signal-to-noise data. Results from examining the Faber-Jackson relation and the Fundamental Plane indicate these objects are not kinematically disturbed relative to more evolved spheroids. A case-study of the internal kinematics of one object in our sample shows it to be pressure-supported and not rotationally-dominated. Overall our results are consistent with merger-induced starburst scenarios where the young population is observed during the later stages of the merger.