;.] LINEAR MOTION. 



CHAPTER I. 



GEOMETRY OF MOTION. 



I. Linear Motion ; Translation and Rotation. 



5. Motion consists in change of position. 



6. We begin with the simple case of a point moving in a 

 straight line. The position of a point P in a line is deter- 

 mined by its distance OP=x from some fixed point or origin, 

 O, assumed in the line, the length x being taken with the 

 proper sign to express the sense (say forward or backward, to 

 the right or to the left) in which it is to be measured on the 

 line. This sense is also indicated by the order of the letters, so 

 that PO=-OP, and OP+PO = o. 



The position of a point in a line is thus fully determined by 

 a single algebraical quantity or co-ordinate ; viz. by its abscissa 

 x=OP. 



7. Let the point P move in the line from any initial position 

 P Q (Fig. i) to any other position P v and let OP =x Q , OP^x v 



This change of position, or displacement, is fully determined 

 by the distance P Q P l =^ 1 x^ traversed by the point. 



Now let this displacement P Q P l be followed by another dis- 

 placement in the same line, from P l to P 2 , in the same sense as 



