52 KINEMATICS. [104. 



that is, in rectilinear motion the acceleration at any point or 

 instant is the value, at that point or instant, of the second deriva- 

 tive of the space with respect to the time. 



Negative acceleration will thus indicate a decreasing veloc- 

 ity. 



104. When the acceleration is constant, the motion is said to 

 be uniformly accelerated. In the case of variable acceleration 

 we might again consider its rate of change, which may be called 

 the acceleration of the second order ; and so on. Compare 

 Art. 156. 



105. Conformably to the definition of acceleration, its unit is 

 the "cm. per second per second" in the C. G. S. system, and 

 the "foot per second per second" in the F. P. S. system. As 

 it can rarely be convenient to use two different time units in the 

 unit of acceleration (say, for instance, mile per hour per second), 

 it is customary to mention the time unit but once and to speak 

 of an acceleration of so many feet per second, or cm. per sec- 

 ond, it being understood that the other time unit is also the 

 second. 



For the dimensions of acceleration we have (see Art. 92) 



Denoting, as in Arts. 93, 94, the concrete value of an 

 acceleration by J t its unit by J lt and similarly for length and 

 time, we have the equation 



J__L_ Tf 



which shows that (a) the numerical value J/J^ of an acceleration 

 varies directly as the square of the unit of time* and inversely 

 as the unit of length ; and (b) the unit of acceleration,^, varies 

 directly as the unit of length, and inversely as the square of the 

 unit of time. 



