134 THE REALITIES OF MODERN SCIENCE 



of energy. For that discussion we shall need a relation- 

 ship between the velocity acquired by a body which 

 is uniformly accelerated and the space over which it 

 passes. 



The scientist uses the word " velocity" to represent 

 speed in a definite direction. For example, a point 

 on a uniformly rotating wheel is moving with constant 

 speed, but its velocity is constantly changing, for the 

 direction of motion is constantly changing. If we are 

 dealing, however, only with motion in a straight line, 

 velocity and speed are identical. Just as velocity is 

 defined as the time-rate of change of position, so 

 acceleration is defined as the time-rate of change of 

 velocity. (In the illustration of the rotating wheel 

 it is evident that each point is constantly accelerated 

 toward the center.) 



The simplest case for analysis is that of a body 

 moving with constant velocity. If the velocity is 

 v it will travel in a time, t, a distance, s, such that 

 s = vt. If the velocity is not constant the simplest 

 case occurs when the acceleration is uniform, that is, 

 when the velocity increases the same number of units 

 of velocity in each unit of time. Let a represent the 

 acceleration, then if the initial velocity is zero the 

 velocity at the end of t seconds is expressed as v=at. 

 (In general, 1 if the initial velocity is not zero but is , 

 then the velocity at the end of t seconds is v = v +at.) 



Because the velocity increases uniformly it follows 

 that the body is moving with its average velocity at 



1 In an ordinary elementary course in physics there occur about 

 twenty physical relations which are entirely analogous to this 

 expression and are represented by similar equations. 



