Question: In his Dialogues Concerning Two New Sciences, Galileo wrote: The distances traversed during equal intervals of time by a body falling from rest stand to one another in the same ratio as the odd numbers beginning with unity. Assume, as is now believed, that s = -(gt2)/2, where s is the total distance traveled in time t, and g is the acceleration due to gravity.
(a) How far does a falling body travel in the first second (between t = 0 and t = 1)? During the second second (between t = 1 and t = 2)? The third second? The fourth second?
(b) What do your answers tell you about the truth of Galileo's statement?