The force opposing the motion of a car is assumed to vary in proportion to the square of the car’s speed. At a speed of $20\,\text{m s}^{-1}$, the force has magnitude $800\,\text{N}$. What effective power must the car’s engine provide to keep the car moving at a constant speed of $40\,\text{m s}^{-1}$?
- A$32\,\text{kW}$
- B$64\,\text{kW}$
- C$128\,\text{kW}$
- D$512\,\text{kW}$