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?

• A. $W_{friction}=\frac{1}{2}mv^2;\ W_{acceleration}=0$
• B. $W_{friction}=\frac{1}{4}mv^2;W_{acceleration}=\frac{1}{4}mv^2$
• C. $W_{friction}=0;\ W_{acceleration}=\frac{1}{2}mv^2$
• D. $W_{friction}=0;\ W_{acceleration}=0$