Leonardo da Vinci, in the fifteenth century, formulated a different law of motion. He proposed that the distances fall in successive equal intervals of time are proportional to the consecutive integers. That is, suppose that, starting from rest, a body falls one foot in the first time interval. Then the body will traverse two feet in the second time interval, 3 feet in the third time interval, etc.
(A) Construct a graph showing the total distance traveled by a falling body starting from rest, according to Leonardo's law and according to Galileo's law. Plot both on the same graph.
(B) Make another graph, showing velocity as a function of time, for both laws. Fundamentally, how do we know Leonardo's law is not correct?
This solution constructs two graphs showing total distance travelled by a falling and the velocity as a function in time to show why Leonardo da Vinci's law of motion is incorrect.