Galileo (1564-1642) wanted to determine how the speed of a falling object changes as it falls. He conducted many free-fall experiments, but he found the motion of a falling object difficult to analyze. Eventually, he came up with the idea that it would be easier to perform experiments with a ball that rolls down a gentle incline, because the speed of the ball would be slower than the speed of a falling object. One objective of Galileo's inclined plane experiments was to determine how the speed of a ball rolling down an inclined plane changes as it rolls. Examine the inclined plane shown below and the time-distance data in the following table.

Elapsed time t, in seconds Distance d, in centimeters (cm), a ball rolls in t seconds (s)

Inclined Plane 1 Inclined Plane 2
0 0 0
1 9 9.5
2 36 38
3 81 85.5
4 144 152
5 225 237.5

For inclined plane 1, the distance a ball rolls in the 1st second is 9 centimeters. Think of this distance as 1 unit. That is, for inclined plane 1,

1 unit = 9 centimeters.
Determine how far in terms of units a ball will roll, on inclined plane 1, in the following time intervals.

a. 2nd second: t = 1 to t = 2 seconds
units
b. 3rd second: t = 2 to t = 3 seconds
units
c. 4th second: t = 3 to t = 4 seconds
units
d. 5th second: t = 4 to t = 5 seconds
units