Several models of variational phase field for fracture have been introduced and analyzed to different degrees of applications, and the rate-independent phase field approach has been shown to be a versatile one, but it is not able to accurately capture crack velocity and dissipated energy in dynamic crack propagation. In this paper, we introduce a novel rate-dependent regularized phase field approach to study dynamic fracture behaviors of polymethylmethacrylate materials, in which the rate coefficient is estimated through energy balance, i.e., dynamics release energy, cohesive energy and dissipated energy. The mode-I dynamics crack problem is considered, and its accuracy is validated with respect to experimental data [F. Zhou, Ph.D. dissertation (The University of Tokyo, Japan, 1996)] and other numerical methods, taking the same configuration, material property, crack location, and other relevant assumptions. The results shed light on the requirement and need for taking the rate-dependent coefficient in dynamic fracture analysis.