A luggage cart with mass $m$ is placed on an airport's moving walkway moving at speed $v$. The kinetic friction coefficient between the cart and walkway is $\mu_{k}$ . Over time $t$, the cart stops moving relative to the walkway, traveling distance $d=\frac12\frac{v^2}{\mu_{k}g}$ . How much of the work done by the walkway's motor is used against friction and how much to accelerate the luggage?