The force that opposes the motion of a car is proportional to the square of the car’s speed. At a speed of $20.0\ \text{m s}^{-1}$, the force has a magnitude of $800\ \text{N}$. What useful output power must the car’s engine provide in order to keep the car moving at a constant speed of $40.0\ \text{m s}^{-1}$?
- A$32\ \text{kW}$
- B$64\ \text{kW}$
- C$128\ \text{kW}$
- D$512\ \text{kW}$