An exact solution of the problem of the unsteady free convection flow of a viscous elec- trically conducting incompressible fluid in the presence of thermal radiation and under the influence of uniform magnetic field applied normal to the plate near an infinite vertical plate, which moves at a time dependent velocity, is presented here by the Laplace transform technique. The fluid is also assumed to be gray; emitting absorbing but non scattering medium and the optically thick radiation limit is considered. The solutions of the present problem were obtained in closed forms with arbitrary magnetic field parameter (M), radiation parameter (F), Prandtl number ( r P ), thermal Grashof number ( r G ), etc. Some important applications of physical interest for different type motion of the plate are discussed. Applying numerical values into the expressions of analytical solution, we also discussed the vertical air flows — the usual phenomenon at plumes into the atmosphere.