One dimensional Lennard-Jones fluids are known to exhibit an interesting 1/t(3) time (t) dependence of the velocity correlation function. The origin of this decay is apparently not well understood. We have studied this problem both by molecular dynamic simulations and by mode coupling theory. We find that this t(-3) decay of the velocity autocorrelation function (VACF) arises from the coupling of the tagged particle's motion to the longitudinal current mode of the fluid. Interestingly such a decay is intern rendered possible by the Gaussian time dependence of the coherent dynamic structure factor at the relevant times. This is confirmed by the simulations of Lennard-Jones rods. The t(-3) dependence is found to be dominant at low and intermediate densities. We show that the mode coupling theory provides an accurate description of the VACF both at short and long time limits.