So 



KINEMATICS. 



[156. 



Dividing this infinitesimal vector by dt, we obtain in general a 



finite magnitude , the geometrical derivative of the 



dt 



velocity with respect to the time, and that is what we call the 

 acceleration at the time t or at the point P. We represent it 

 geometrically by a vector j drawn frotn P parallel to the direc- 

 tion of Km VV. 



It will be noticed that the sense of the acceleration will be 

 towards that side of the tangent of the curve on which the 

 centre of curvature is situated. 



156. Suppose a point P to move along a curve P^P^P^ ...i 

 with variable velocity v (Fig. 38). From any fixed origin O\ 

 draw a vector OV l = v lJ equal and parallel to the velocity v^ ofj 



P lt and repeat this construction for every position of the mov- 

 ing point P. The ends P\, V^ V& ... of all these radii vectores 

 drawn from O will form a continuous curve V^V^Y^... which is 

 called the hodograph of the motion of P. 



If we imagine a point V describing this curve V^V^V^... at 

 the same time that P describes the curve P^PJP^ . .., it is evident 



that the velocity of V t i.e. fi 



dt 



! , laid off on the tangent of I 



the curve 



..., represents the acceleration of the point 



