CHAPTER III. 



VELOCITY AND ACCELERATION. 



28. Displacement. Let #, y, z be the coordinates of a 

 moving point at any particular instant with reference to any 

 particular frame, x, y', z the coordinates of the point at a 

 subsequent instant, with reference to the same frame, then x r - x, 

 y' y, z' z are the components, parallel to the axes, of a vector 

 quantity called the displacement of the point. The vector is not 

 localised. 



29. Velocity in a straight line. Consider in the first place 

 a point moving in a straight line, e.g. one of the lines of reference, 

 and let s be the number of units of length it passes over in t units 

 of time. Then it may happen that the two numbers s and t have 

 a constant ratio whatever number we take for t. The point is then 



m 



said to move uniformly in the line, and the fraction - is defined to 



t 



be the measure of its velocity. A point moving uniformly 

 describes equal lengths in equal times. 



Again consider the case where the point moves in a straight line, but the 

 number of units of length passed over in any interval of time does not bear a 

 constant ratio to the number of units of time in the interval. In this case 

 there will be equal intervals of time in which the point describes unequal 

 lengths ; in the one of two equal intervals in which it describes the greater 

 length we should say it was moving faster, in the other, in which it describes 

 the shorter length, we should say it was moving more slowly. We have thus 

 an idea of velocity of a point not moving uniformly, let us try to make it 

 precise. 



