Galileo, in his masterwork Dialogues Concerning Two New Sciences discusses free fall motion and…

Galileo, in his masterwork Dialogues Concerning Two New Sciences discusses free fall motion and writes: When, therefore, I observe a stone initially at rest falling from an elevated position and continually acquiring new increments of speed, why should I not believe that such increases take place in a manner which is exceedingly simple and rather obvious to everybody? If now we examine the matter carefully we find no addition or increment more simple than that which repeats itself always in the same manner. This we readily understand when we consider the intimate relationship between time and motion; for just as uniformity of motion is defined by and conceived through equal times and equal spaces (thus we call a motion uniform when equal distances are traversed during equal time-intervals), so also we may, in a similar manner, through equal time-intervals, conceive additions of speed as taking place without complication; thus we may picture to our mind a motion as uniformly and continuously accelerated when, during any equal intervals of time whatever, equal increments of speed are given to it. Thus if any equal intervals of time whatever have elapsed, counting from the time at which the moving body left its position of rest and began to descend, the amount of speed acquired during the first two time-intervals will be double that acquired during the first time-interval alone; so the amount added during three of these time-intervals will be treble; and that in four, quadruple that of the first time-interval. Question: in this excerpt, Galileo tries to show that:

a.A free falling object continues to fall with the same speed that it gains after one second. So, if its speed after a second is X, it falls with the same speed X all the way down.

b.A free falling object’s speed varies based on its shape and volume, which are two main parameters defining the amount of friction of the object with air.

c.free falling object travels equal distances every second

d.A free falling object’s speed increases in a constant increment or it accelerates in a constant rate

e.Both a. and c. are correct

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