j I3-] RECTILINEAR MOTION. 55 



111. If in addition the initial velocity V Q be zero, the point 

 .starting from rest at the time ^=o, the equations reduce to the 

 following : 



v=jt, (6") 



" : ,. (7") 



;* ." ' (8") 



112. The most important example of. uniformly accelerated 

 motion is furnished by a body falling in vacuo near the earth's 

 surface. Assuming that the body does not rotate during its 

 fall, its motion relative to the earth is a mere translation, and 

 it is sufficient to consider the motion of any one point of the 

 body. It is known from observation and experiment that under 

 these circumstances the acceleration of a falling body is con- 

 stant at any given place and equal to about 9^0 cm., or 32 ft., 

 per second per second. ; the value of this so-called acceleration 

 of gravity is usually denoted by g. 



In the exercises on falling bodies (Art. 114) we make through- 

 out the following simplifying assumptions : the falling body 

 does not rotate ; the resistance of the air is neglected, or the 

 body falls in vacuo ; the space fallen through is so small that 

 g may be regarded as constant ; the earth is regarded as fixed, 

 i.e. we consider only the relative motion of the body with respect 

 to the earth. 



,. 



113. The velocity v acquired by a falling body after falling 



from rest through a height h is found from (8") as 



This is usually called the velocity due to the height (or head) h, 



while 



is called the height (or head) due to the velocity v. 





