38 ELEMENTARY GENERAL SCIENCE CHAP. 



EXAMPLE. A train, travelling at a uniform rate, completes 

 a distance of 10 miles in 15 minutes ; what is its velocity in 

 feet per second '( 



Answer : 10 miles = 10 x 1,760 x 3 feet = 52,800 feet 

 15 minutes = 15 x 60 = 900 seconds 



. ' , since r = 



52,800 P0 o r 



v = _ _ = 58^ feet per second, 

 VMK) 



or the train travels at a uniform velocity of 58| feet in every 

 second. 



Acceleration. An express train starting from a terminus 

 begins to move slowly, and, as the journey proceeds, the rate of 

 motion goes on increasing until it gets its full speed. A stone 

 let fall from a height similarly starts from rest, and as it moves 

 it goes faster and faster until brought to a standstill again on 

 reaching the ground. Or we might imagine a cyclist starting for 

 a run, and regularly increasing his speed until he could not go 

 any faster. In all these examples the velocity of the moving 

 body has regularly increased and the rate at which the change has 

 taken place is spoken of as acceleration. 



Acceleration is the Rate of Change of Velocity. But it 

 may be of an exactly opposite kind to the instances given above. 

 Reverse each of the examples and consider what happens. An 

 express train going at full speed approaches a station and its 

 velocity is regularly diminished until it is brought to rest at the 

 platform. A stone is thrown upwards with a certain velocity, it 

 moves more slowly and more slowly until it comes to rest, and 

 then starts falling. A cyclist travelling at full speed slackens 

 his rate regularly until he comes to a standstill. In all these 

 cases we have examples of an acceleration of an exactly opposite 

 kind to the previous instances, but yet an acceleration. In 

 ordinary language this kind of acceleration is given a name of its 

 own, retardation. 



Measurement of Uniform Acceleration. In measuring a 

 regular or uniform acceleration, we must know what addition to or 

 subtraction from the velocity of the moving body there has been 

 during each second of its journey. Suppose there is an addition 

 of one foot per second to the velocity of a moving body, and 

 that it has taken one second to bring about this change, we 



