ID;.] RECTILINEAR MOTION. 53 



106. Exercises. 



1 i ) A point moving with constant acceleration gains at the rate of 

 30 miles an hour in every minute. Express its acceleration in F. P. S. 

 units. 



(2) At a place where the acceleration of gravity is g= 9.810 metres 

 per second, what is the value of g in feet per second ? 



(3) A railroad train, 10 minutes after starting, attains a velocity of 

 45 miles an hour; what was its average acceleration during these 10 

 minutes ? 



(4) If the acceleration of gravity, g= 32 feet per second, be taken 

 as unit, what is the acceleration of the railroad train in Ex. (3) ? 



3. APPLICATIONS. 



107. Uniformly Accelerated Motion. As in this case the accel- 

 eration/is constant (see Art. 103), the equation of motion (5) 



can readily be integrated : 



v=jt+C. 



To determine the constant of integration C, we must know the 

 value of the velocity at some particular moment of time. Thus, 

 if V = V Q when /=o, we find v Q =C; hence, substituting this 



value for C, 



v v Q =jt. (6) 



This equation, which agrees with the definition of / given in 

 Art. 103, gives the velocity at any time t. Substituting ds/dt 

 for v and integrating again, we find s = v Q t+^jfi+C , where the 

 constant of integration, C, must again be determined from 

 given "initial conditions." Thus, if we know that S=S Q when 

 /=o, we find s Q =C' ; hence 



(7) 



