In his free-fall experiments using an inclined plane, galileo established a few key ideas regarding uniformly accelerated motion. this problem explores three of his findings assume that the object starts at rest (a) formally show that for an object in free fall along the y-direction, the total distance traveled with respect to the initial position, yo is increasing as the square of the number of (equal) time steps, δ, to the respective point. in other words, if t.-im , work out the ratio, y-y , where y, is the position of the object at time t (b) show that the distance traveled during each successive time interval, δ, when divided by the distance traveled during the first time interval, y, -yo. leads to the series of odd numbers (c) show that the average speed on each successive time interval is increasing in proportion to the series of odd numbers