Final answer:
Doubling your speed causes the centripetal acceleration to increase by a factor of four, not six, and the same is true for the braking distance, which increases due to the squared relationship with speed.
Step-by-step explanation:
When you double your speed, the centripetal acceleration and hence the centrifugal force you experience in a curve indeed increases, but not sixfold. The centripetal acceleration is proportional to the square of the velocity, which means that if you double your speed, the centripetal acceleration (and thus the force if the mass is constant) increases by a factor of four, not six.
Furthermore, while the breaking distance does increase with speed, it isn't directly connected to centripetal force or acceleration. The increase in braking distance is due to the energy that must be dissipated, which goes up with the square of the speed. Therefore, doubling the speed would also roughly quadruple the stopping distance, assuming the same constant deceleration, but real-world factors may cause this to vary.