A motor drives a conveyor belt so that it moves with velocity $v$. Sand falls straight down onto the belt at a rate of $m\,\text{kg s}^{-1}$. What extra power is required to keep the conveyor belt moving at constant speed when the sand begins to land on it?
- A$\tfrac{1}{2}mv$
- B$mv$
- C$\tfrac{1}{2}mv^2$
- D$mv^2$