40 ELEMENTARY GENERAL SCIENCE CHAP. 



formula or expression we have just given will become modified. 

 Imagine a body moving with a uniform velocity of u units per 

 second to have this velocity uniformly accelerated. Let the 

 acceleration be a units, as in the case of the body moving from 

 rest. Then, at the end of the first second during which the 

 acceleration acts its velocity will be u + , at the end of the 

 second second it will ben + 2a, at the end of the third u + .')a, 

 and at the end of t seconds u + ta or n + at, or the formula becomes 



v = u + at. 



EXAMPLE. What will be the velocity of the engine in the 

 last example at the end of the sixth minute, if it continues to 

 move with the same acceleration ? 



At the end of fifth minute its velocity u = 600 feet per second. 

 And v = u + at 



= 600 + (2 x 60) 

 =5 720 feet per second. 



Space traversed by a Body moving under the influence 

 of a Constant Acceleration. The space travelled over by a 

 body in one second is equal to its average velocity, and that tra- 

 velled over in t seconds is equal to its average velocity multiplied 

 by t . If it starts from rest and travels for one second finishing 

 with a velocity of v feet per second, its average velocity is -i r 

 during this time, and 



Substituting value of v from the equation v = at, we get 



s = t xt 



or since t = we can write the equation s = %rt thus 



T' T^ 



s = v x - = i , from which 



a - 



v 2 = 2as. 



Expressed in words, the rule for finding the space travelled in 

 a given number of seconds is multiply half the acceleration 

 (expressed in feet per second per second) by the square of the 

 number of seconds through which the body travels and wo 

 ascertain the number of feet passed over by the body. 



The last equation of all provides us with a rule for calculating 

 the velocity of a body after it has travelled over a certain 

 distance under the influence of a uniform acceleration ; it tells 

 us that the square of the body's velocity is equal to twice the 



