Although static potentials have long been used in nuclear models, and reproduce many experimental results remarkably well, they do not satisfy certain physical requirements. It is shown that for single-particle problems at a fixed energy, some static potential will always give the same results as any velocity-dependent potential. Furthermore, if the velocity-dependent potential is assigned a certain type of functional form, including the commonly used one proposed by Woods and Saxon, the equivalent static potential has nearly the same form. Thus, it is very difficult to test for velocity-dependence by means of elastic scattering and energy-level calculations. The effect of velocity-dependence on inelastic scattering is not established analytically, but numerical calculations imply that it would also be extremely difficult to detect.