9 i.] VELOCITY. 45 



II. Linear Kinematics. 



I. UNIFORM RECTILINEAR MOTION; VELOCITY. 



88. Consider a point moving in a straight line. If through- 

 out the whole motion equal spaces are always described in equal 

 times, the motion is said to be uniform. 



89. Next consider two points each moving uniformly in a 

 straight line. The motions may still be different ; for it is pos- 

 sible that while one of the points moves in a given time t over a 

 space s v the other moves during the same time / over a different 

 space s 2 . The points are then said to have different velocities, 

 .and their velocities are said to be as s l is to s 2 . The velocity v 

 of uniform motion is therefore measured by the ratio of the 

 .space s described in any time t to this time ; that is, v=s/t. 



90. This equation written in the form 



s = vt (i) 



is called the equation of motion of the point. It follows from 

 Art. 89 that in uniform motion the velocity v is constant. 



With t as abscissa and s as ordinate (or vice versa], the equa- 

 tion of uniform motion (i) represents a straight line ; the 

 tangent of the angle made by this line with the axis of / repre- 

 sents the velocity v. 



91. Let the point P start at the time t=o from a point O 

 (Fig. 27); let it reach the point P Q at the time t=t Q and the 



Fig. 27. 



point P l at the time t=t. Then, putting OP Q =s Q) OP l = s, the 

 space passed over in the time t t Q is s J ; hence the velocity 

 v=(s s^)/(t t^. The equation of uniform motion can there- 

 fore be written in the form 



