MATHEMATICAL REPRESENTATION OF VECTOR 441 



It is evident that when / 



,/fl 

 Also 



10-02 -3- = 195. 

 8007C 



tit 180 



13-90 



the angle being expressed in radians, 



a - = 105-7 x 13-96 = 1476 

 at 



Then 



drtf / dO\ 2 

 J + ( a ft) = 



+ 147fi2 



1489 



1476 

 tan a ==7-568 



a = 82 28' 



Thus when t = 10-02 the magnitude of the acceleration is 1489 

 ft. per sec. per sec., and its direction makes an angle of 82 28' 

 with the direction of the corresponding velocity. 



It also makes an angle of 124 28' with the fixed line. 



Example 2. The velocity of a body is continually changing in 

 direction and magnitude. The values given in the table below 

 give p, the magnitude, and 0, the direction measured from a fixed 

 line, at any time t seconds. Find the value of the acceleration 

 when t = 5-3. 



