Chapter 12 - Section 12.5 - Tangential and Normal Components of Acceleration - Exercises - Page 668: 1

$a =0 \ T +|a| \ N$

$v(t)=\dfrac{dr}{dt}=-a \sin t \ i +(a \cos t) j +b k $ or, $|v(t)|=\sqrt {a^2+b^2}$ Now, $a(t)=\dfrac{d \ v(t)}{dt}=-a \cos t i +(-a \sin t) j + (0) k$ and $|a(t)|=\sqrt {a^2(\cos^2 t+\sin ^2 t)} $ or, $|a(t)|=a$ $a_{N}=\sqrt {|a|^2 -a^2_{T}}=\sqrt {a^2-0}=|a|$ and $a =a_T T+a_{N}=0 \ T +|a| \ N$