| (1) No. of seconds | (2) Total distance moved | (3) Distance each second | (4) Velocity at end of second | (5) Acceleration each second |
| Per second | Per second | |||
| 1 | 30 cm. | 30 cm. | 60 cm. | 60 cm. |
| 2 | 120 cm. | 90 cm. | 120 cm. | 60 cm. |
| 3 | 270 cm. | 150 cm. | 180 cm. | 60 cm. |
| 4 | 480 cm. | 210 cm. | 240 cm. | 60 cm. |
Column 5 shows that the acceleration is uniform, or the same each second. Column 4 shows that the velocity increases with the number of seconds or that V = at. Column 3 shows that the increase in motion from 1 second to the next is just equal to the acceleration or 60 cm. This is represented by the following formula: s = 1/2 a(2t - 1).
The results of the second column, it may be seen, increase as 1:4:9:16, while the number of seconds vary as 1:2:3:4. That is, the total distance covered is proportional to the square of the number of seconds.
This fact expressed as a formula gives: S = 1/2at2.
Substituting g, the symbol for the acceleration of gravity, for a in the above formulas, we have: (1) V = gt, (2) S = 1/2gt2, (3) s = 1/2g(2t - 1).
99. Laws of Falling Bodies.—These formulas may be stated as follows for a body which falls from rest:
1. The velocity of a freely falling body at the end of any second is equal to 32.16 ft. per sec. or 980 cm. per second multiplied by the number of the second.
2. The distance passed through by a freely falling body during any number of seconds is equal to the square of the number of seconds multiplied by 16.08 ft. or 490 cm.
3. The distance passed through by a freely falling body during any second is equal to 16.08 feet or 490 cm. multiplied by one less than twice the number of the second.