440 



PRACTICAL MATHEMATICS 



That is, the acceleration is of magnitude and its direction is 



at right angles to the direction of the velocity. Now the direction 

 of the velocity at any instant is along a tangent, hence the direction 

 of the acceleration is along the corresponding radius. Thus if a 

 body describes a circular path of radius r ft., with uniform velocity 



v z 



v ft. per sec., the acceleration is ft. per sec. 2 , and is directed to- 

 wards the centre. 



213. Example 1. The value of a vector may be stated as a e where 

 a is the amount and 6 is the angle measured anti-clockwise from 

 a found direction. The vector keeps in a plane. A point has 

 the following velocities in feet per second at the following times 

 (seconds). (B. of E., 1911.) 



Find approximately the value of the acceleration when t = 10-02. 

 Now velocity = a (cos 6 + i sin 6) 



l(da\ z / d6\ 2 , 



and acceleration = A/ ( -j- ) + ( a -5- ) {cos (0 + a) + * sin (0 + a) } 

 " \dt/ \ dtj 



where 



tan a = a 



dt Ida 

 1 dt 



