When you boil potatoes does the length of time it takes to cook them depend on how vigorously water is boiling?

No, the length of time it takes to cook potatoes does not depend on how vigorously the water is boiling. The boiling point of water is 100 degrees Celsius (212 degrees Fahrenheit) at sea level, and this temperature does not change regardless of how vigorously the water is boiling. The time it takes to cook potatoes depends on the size and type of potato, as well as the amount of water used.