Accelerated Cops and Robbers

We consider a variant of Cops and Robbers in which both the cops and the robber are allowed to traverse up to $s$ edges on each of their turns, where $s\ge 2$. We give several general for this new model as well as establish bounds for the cop numbers for grids and hypercubes. We also determine the capture time of cop-win graphs when $s=2$ up to a small additive constant.