Substituting _g_, the symbol for the acceleration of gravity, for _a_ in the above formulas, we have: (1) _V_ = _gt_, (2) _S_ = 1/2_gt_², (3) _s_ = 1/2_g_(2_t_ - 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. Important Topics 1. Falling bodies. 2. Galileo's experiment. 3. Acceleration due to gravity. 4. Laws of falling bodies. Exercises 1. How far does a body fall during the first second? Account for the fact that this distance is numerically equal to half the acceleration. 2. (a) What is the velocity of a falling body at the end of the first second? (b) How far does it fall during the second second? (c) Account for the difference between these numbers. 3. What is the velocity of a falling body at the end of the fifth second? 4. How far does a body fall (a) in 5 seconds (b) in 6 seconds (c) during the sixth second? 5. (a) What is the difference between the average velocity during the sixth second and the velocity at the beginning of that second? (b) Is this difference equal to that found in the second problem? Why? 6. A stone dropped from a cliff strikes the foot of it in 5 seconds. What is the height of the cliff? 7. Why is it that the increased weight of a body when taken to higher latitudes causes it to fall faster, while at the same place a heavy body falls no faster than a light one? 8. When a train is leaving a station its acceleration gradually decreases to zero, although the engine continues to pull. Explain. 9. Would you expect the motion of equally smooth and perfect spheres of different weight and material to be equally accelerated on the same inclined plane? Give reason for your answer. Try the experiment. 10. A body is thrown upward with the velocity of 64.32 ft. per sec. How many seconds will it rise? How far will it rise? How many seconds will it stay in the air before striking the ground? 11. 32.16 feet = how many centimeters? 12. The acceleration of a freely falling body is constant at any one place. What does this show about the pull which the earth exerts on the body? (7) THE PENDULUM