A series of hypervelocity impact experiments were conducted at NASA Ames Vertical Range, using spherical copper projectiles and polycrystalline dolomite targets. The intensities of atomic lines and molecular bands in the first 2 microseconds after each impact were measured using a high-speed spectrometer system and assessed as functions of impact velocity (2--5.5 km/s) at a fixed impact angle (45¿ from the horizontal). Although the measured emission intensities follow power law relations well, the power law exponents of individual emission lines and bands are very different, ranging from 2.1 to 9.1. In contrast, the exponent for wavelength-integrated visible light intensity (435--650 nm) is about 5. Such a large variation in exponents suggests a complex nature for the power law relations. In order to understand the physical processes controlling the power law relations, a theoretical model is developed considering chemical equilibrium of both molecular and atomic species, the electronic excitation of atoms, and ionization. This model accounts for the observed variety of the power law exponents well. Such a model will provide a physical framework for predicting the emission intensities from both artificial and natural impacts on planetary surfaces and for estimating size of an impactor from the emission intensity.