This paper investigates frictional dynamic contact mechanics of a functionally graded half-plane subjected to moving contact by a rigid flat punch possessing subsonic, transonic and supersonic speeds. The shear modulus along the half-plane is expressed by an exponential function, and the Poisson's ratio is assumed constant along the graded half-plane. Governing partial differential equations are derived based on the planar theory of elastodynamics. Boundary conditions are applied, and displacement fields in the graded half-plane are determined analytically. Formulation for the contact problem is reduced to a singular integral equation involving Cauchy singularity and a Fredholm kernel. Singular integral equation is solved numerically utilizing a suitable collocation technique. Contact stresses and normalized punch stress intensity factors are calculated for prescribed subsonic, transonic and supersonic speeds of the moving punch. It is expected that the results obtained by this study will help to understand the contact behavior and the surface failure mechanisms of functionally graded materials, especially at transonic and supersonic sliding speeds.