v MATTER IN RELATION TO MOTION C3 



earth is consequently only a particular case of the general rule 

 which has already been learnt by the student. We have a con- 

 stant force, tlmt, viz., equal to the attractive force of the earth, 

 causing a constant acceleration of 32 feet per second in every 

 second, which is, as we have seen, the value of the acceleration 

 due to gravity, y. All we have to do, therefore, is to substitute 

 fj for a in each of the equations on p. 40, and we get : 



v = gt ...................... (1) 



S = igt 2 ................... (2) 



V 2 = 2gs ........... . ......... (3) 



Velocity of a body falling from rest after " t " seconds. 



The first of the above equations provides us with an expression 

 by means of which, knowing the number of seconds, (), for 

 which a body has been moving freely towards the earth under 

 the constant acceleration (g) due to the force of gravity, we can 

 calculate the velocity with which it is moving at a given moment. 



EXAMPLE. With what velocity is a body moving which 

 starting from rest has travelled for 10 seconds ? 



Here we have to find .*, knowing the value of both g and f. 



= 32 x 10-320 feet per second. 



Distance travelled by a Body falling from Rest in "t" 

 Seconds. The second equation at once enables us to determine 

 the distance through which a body, falling freely towards the 

 earth, has moved after it has been travelling for a known number 

 of seconds. 



EXAMPLE. Through how many feet does such a body fall 

 in 30 seconds ? 



Here s = ^ gt 2 



= | x 32 x (30) 2 

 = i x 32 x 900 

 = 14,400 feet. 



Velocity of a Body falling from Rest after moving through 

 Feet. Equation (3) shows how the velocity of a body, which 



starts falling from rest, can be determined when the number of 



feet through which it has fallen is known : 



