This paper studies the thermal radiation and mass transfer effects on unsteady MHD flow past an impulsively started exponentially accelerated vertical plate with variable temperature and also with variable mass diffusion in the presence of transverse applied magnetic field. The fluid considered here is a gray, absorbing/emitting radiation but a non-scattering medium. At time  the plate temperature and concentration levels near the plate raised linearly with time t. The governing equations are solved in closed form by the Laplace transform technique. The velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer are studied graphically while the skin-friction is presented through numerical evaluations for different physical parameters like radiation parameter, magnetic field parameter, Schmidt parameter, Prandtl number, thermal Grashof number, mass Grashof number, accelerating parameter and time.