1 1 6.] RECTILINEAR MOTION. $y 



upward from the point B, with an initial velocity v . (a) When and 

 (&) where will they collide ? (c) If they are to meet at the height -J- h, 

 what must be the initial velocity ? 



115. The general problem of rectilinear motion requires the 

 integration of the differential equation 



where j is a function of s, t, and v, in connection with the 



equation 



ds , x 



As these two equations involve four quantities t, s, v,j, a 

 third relation between them, say 



f(t,s,v,j)=o, (9) 



is always necessary in order to express three of these four 

 quantities in terms of the fourth. Next to the case of uni- 

 formly accelerated motion where the relation (9) is simply 

 /= const., the most important cases are those when/ is given 

 as a function of s, or of v, or of both s and v. 



116. Whenever in nature we observe a motion not to remain 

 uniform, we try to account for the change in the character of 

 the motion by imagining a special cause for such change. In 

 rectilinear motion, the only change that can occur in the 

 motion is a change in the velocity, i.e. an acceleration (or retar- 

 dation). The cause producing acceleration or retardation we 

 call force (attraction, repulsion, pressure, tension, friction, resist- 

 ance of a medium, elasticity, cohesion, etc.), and assume it to 

 be proportional to the acceleration. A fuller discussion of the 

 nature of force and its relation to mass will be found in Chapter 

 III., II. The present remark is only intended to make more 

 intelligible the physical meaning and applications of the prob- 

 lems to be discussed in the following articles. 



