S 8 



KINEMATICS. 



[117. 



117. Acceleration inversely proportional to the square of the dis- 

 tance, i.e. j=^i/s i where //, is a constant (viz. the acceleration at 

 the distance s=i) and s is the distance of the moving point 

 from a fixed point in the line of motion. 



The differential equation (5) becomes in this case 



(II 



the first integration is readily performed by multiplying botl 

 members by ds/dt so as to make the left-hand member th< 

 complete derivative of \(ds/dt)* or ^v 2 . Thus we find 



-,+<: +c, 



where the constant of integration, C, must be determined froi 

 the so-called initial conditions of the problem. For instanc< 

 if V = VQ when s=s Qt we have J^ 2 = fJL/s Q +C', hence, eliminat- 

 ing C between this relation and (i i), 



To perform the second integration, we solve this equation f( 

 v and substitute ds/dt for v : 



or putting v + 2 /A/J O = 2 



dt /i S 



Here the variables s and / can be separated, and we find 



