58 APPLIED SCIENCE 



total distance fallen through at the end of any given second is 

 equal to the average velocity up to the given point multiplied 

 by the number of seconds during which the object has fallen. 



For example: 



Initial velocity = 00.0 ft. per sec. 



Velocity at end of 3rd. sec. = 96.6 " " " 



2) 96.6 



Average velocity for first 3 sec. = 48.3 " " " 



3 X 48.3 = 144.9 ft., space fallen through in first 3 sec. 



The above theory supposes a body to be falling freely in 

 a vacuum, but while the air will offer a resistance and some- 

 what reduce the actual motion the principle is the same. 

 Acceleration due to gravity varies but little at different 

 latitudes of the earth. Acceleration due to gravity decreases 

 at higher altitudes, and increases as we go below the surface 

 of the earth. All these variations on the earth's surface are 

 so small that they hardly need to be considered in any cal- 

 culation concerning practical problems in mechanics. Ac- 

 celeration due to gravity may be considered as 32.2 ft. per 

 second each second. 



Since the velocity of falling bodies increases at the uniform 

 rate of 32.2 ft. per second, the final velocity in feet per 

 second must equal the product of the time in seconds multi- 

 plied by 32.2. 



To illustrate the calculation: What final velocity will a body 

 acquire in a free fall during 7 seconds? 



I' 7 X 32.2 - 225.4 ft. per second 



59. Kinds of Motion. Motion may be uniform or variable. 

 When equal distances are traversed or covered in the same 



