<p>Wormholes are hypothetical shortcuts through spacetime, have fascinated cosmologists and theoretical physicists for decades. In this paper, traversable wormholes were studied in the static as well as dynamic backgrounds, with particular stress on cosmic time-dependent wormhole. A concerted effort is made to provide an evolving wormhole shape function, which is both radially (<i>r</i>) and cosmic time (<i>t</i>) dependent. Also, wormholes, which appear as special solutions to the EF equations, are now being viewed as viable interstellar objects. A new matter source, which supplies fuel to construct wormhole spacetime, is provided. Exact wormhole solutions were found in the model under static and dynamic background geometries. It is shown that the exotic matter, which is the necessary ingredient for wormhole physics violate the null and strong energy conditions, but obey the weak and dominant energy conditions marginally in the static case. However, in the dynamic case, the exotic matter, which is the necessary ingredient for wormhole physics, violates the dominant energy conditions, satisfies the null and weak energy conditions partially and fully satisfies the strong energy conditions. Further, stability analysis in each case suggests that the wormhole is traversable in both the cases. Some physical features are briefly discussed in this paper.</p>