4 6 KINEMATICS. [92. 



If the times be counted from the instant when the moving 

 point is at P Q , we have / =o, and the equation of motion is 



Finally, if both times and spaces are counted from P Q as 

 origin, we have J = o, so that (i") reduces to (i). 



92. To measure velocities we must adopt a unit of velocity. 



In kinematics, the only fundamental, i.e. independent, units 

 required are those of length and time. All other quantities 

 can be expressed in terms of length and time, and their units 

 are therefore called derived units. 



Thus, the definition of the velocity of uniform motion as a 

 length divided by a time (Art. 89) can be expressed by the 

 symbolic equation 



and we say that the dimensions of velocity are I in length and 

 i in time. 



When L = l and T = l, we have V = l. We must therefore 

 select for our unit of velocity that velocity with which unit 

 length is described in unit time. 



Hence in the C. G. S. system (see Arts. 13, 14) the unit 

 velocity is a velocity of i cm. per second ; in the F. P. S. system 

 it is a velocity of i ft. per second. 



93. In practice other units are often used, and the same 

 concrete velocity can therefore be expressed by different num- 

 bers. Thus the same velocity of a railroad train can be 

 described as 30 miles per hour, or 44 ft. per second, or (approx- 

 imately) 13.41 metres per second. 



The symbols s, v, t, etc., in the kinematical equations must be 

 understood to represent the numerical ratios of the concrete 

 quantities to their respective units. The symbol v, for instance, 

 stands for the ratio V/Vi of the concrete velocity Fto its unit 



