2 THE HUMAN MOTOR 



datum. A man walking moves, relatively to the earth surface, 

 the earth itself being in motion. The earth is moving relatively 

 to the sun, while the sun also moves in space. 



Let the moving body be' considered as a point. In moving, 

 the point traces out a path which may be straight or curved. 

 Its motion is either uniform or variable according as to whether 

 the space passed over in equal intervals of time is the same or 

 differs from time to time in its progress. 



The unit of time being the " second," the speed in the case of 

 uniform motion is the space traversed in one second. Denote 

 the speed by " v." At the end of " / " beconds the body will 

 have passed" through a space given by the equation. 



s = vt. 



This is the fundamental equation for a body moving at a 

 constant speed. 



If the motion is variable the speed must increase or decrease 

 from one moment to another. 



This increase of speed is called " acceleration " and is denoted 

 by the symbol "/" Tne acceleration is the rate of change of 

 velocity. It may be positive if the speed increases, or negative 

 if it decreases. 



If we want to find the true speed of a moving body at any given 

 instant we must take an infinitely short period of time and find 

 the space traversed in this period. Using the notation of the 

 differential calculus, we write that the speed v. 



ds 



V =di 

 i.e., the speed is the differential of space with regard to time. 



In the same way the acceleration " f", which is the rate of 

 change of velocity, can be represented by the equation. 



, dv 



f = 



dt 



A simple and common case is that of uniform acceleration ; 

 the speed increases or decreases in equal quantities in equal 

 times. If a body is allowed to fall, the speed is zero at the moment 

 of release, / at the end of 1 second, and ft at the end of t seconds. 

 The average speed then is : 



+ /' 



~2~ 



Everything happens exactly as if the body fell with a uniform 

 movement not varied and at the speed v m . The space covered 

 5 = v m X t will be 



s = \ft X / = \}t\ 



