  We define a total order, which we call rooted order, on minimal generating
set of $J(P_n)^s$ where $J(P_n)$ is the cover ideal of a path graph on $n$
vertices. We show that each power of a cover ideal of a path has linear
quotients with respect to the rooted order. Along the way, we characterize
minimal generating set of $J(P_n)^s$ for $s\geq 3$ in terms of minimal
generating set of $J(P_n)^2$. We also discuss the extension of the concept of
rooted order to chordal graphs. Computational examples suggest that such order
gives linear quotients for powers of cover ideals of chordal graphs as well.
