In contrast to the extensive studies on static target pointing, much less formal understanding of moving target acquisition can be found in the HCI literature. We designed a set of experiments to identify regularities in 1D unidirectional moving target selection, and found a Ternary-Gaussian model to be descriptive of the endpoint distribution in such tasks. The shape of the distribution as characterized by μ and ω in the Gaussian model were primarily determined by the speed and size of the moving target. The model fits the empirical data well with 0.95 and 0.94 R2 values for μ and ω, respectively. We also demonstrated two extensions of the model, including 1) predicting error rates in moving target selection; and 2) a novel interaction technique to implicitly aid moving target selection. By applying them in a game interface design, we observed good performances in both predicting error rates (e.g., 2.7% mean absolute error) and assisting moving target selection (e.g., 33% or a greater increase in pointing accuracy).