in TIME, VELOCITY AND ACCELERATION 39 



should refer to this as an acceleration of one foot per second in 

 a second, or one foot per second per second. An acceleration which 

 increases the velocity is referred to as positive, while that which 

 diminishes it is negative. The first examples given above are 

 instances of positive acceleration, while when we reverse them 

 they afford cases of negative acceleration. 



Unit of Acceleration. As in every other measurement so, 

 when \ve wish to measure accelerations, we must have a unit in 

 terms of which we can express the quantity under consideration. 

 The unit of acceleration is the increase of unit velocity in a 

 unit of time ; it is generally taken as equal to an increase of 

 velocity of one foot per second per second. An acceleration of two 

 units would thus be an increase of velocity of two feet per second 

 per second, and, similarly, an acceleration of three units equals 

 an increase of velocity of three feet per second per second, an 

 acceleration of a units equals an increase of velocity of a feet 

 per second, in one second. 



If we wish to determine the velocity at any instant of a body 

 which is moving with a uniformly accelerated velocity we must 

 argue as follows : Let the acceleration be a, which means an 

 increase of velocity of a feet per second in one second. Suppose 

 a body starts from rest, at the end of the first second it has a 

 velocity of a feet per second, at the end of the next second 2a, at 

 the end of t seconds at feet per second. Or if r change of velocity 

 in t seconds, we can write 



v = at. 



Consequently, to find the velocity at any instant of a uniformly 

 accelerated moving body, all we have to do is to multiply the 

 number of units of acceleration by the number of units of time 

 for which it has been moving. 



EXAMPLE. An engine moves from rest with a uniform 

 acceleration of 2 feet per second in every second. What is its 

 velocity at the end of 5 minutes ? 



/ 



5 minutes = 5 x 60 = 300 sees. 

 Here a = 2 ; t = 300 ; v = ? 

 But v = at 



= 2 x 300 = 600 feet per second. 



If the uniform acceleration is applied to a body already 

 moving with a uniform velocity, it is not difficult to see that the 



