Actually, the power required is more than squared, closer to cubed. To go 200 mph requires something closer to eight times rather than just four times the power. You have the normal squared relationship you expect plus the greater weight of the air that must be pushed aside. This is why, while it is possible to hit 200 mph with around 500 HP, 1000 Hp won't get you to any more than about 250 mph, and it takes well over 1700 to hit 300 - only 1.5 times as fast, but it takes about 1.5 cubed or 3.4 times as much power required to reach it.
"If no one has ever done it that way, it might be fun to try."