  In this paper we study the dynamics of $\varphi^{4}$ kinks, generated by
considering a particular argument of $\varphi^{4}$ field, in the presence of
class of smooth space dependent potentials ie. barriers and wells. Various type
of these potentials are produced via two-parameter family. These parameters
control the shapes, widths and heights of such potentials. The dynamics are
presented through the plotting of the trajectories. We compare numerical
calculated critical velocities to theoretical calculations.
