Railgun is a multiphysical device which propels a rigid object (the armature) with the electromagnetic force. The electric current flowing in rails forms an electromagnetic field that depends upon material properties (conductivity) of the railgun and the surrounding air. As the armature moves, the conductivity changes which makes the electromagnetic field evolve along with the induce force. This project is concerned with the study of a two-dimensional model of the railgun in which the eddy current version of Maxwell equations, expressed in terms of potentials, is coupled with the Newton's law of motion for the armature. The coupled problems is discretized using hp-adaptive edge finite elements and a one-step implicit Euler method. The project is financed by Institute of Advanced Technology (IAT).