Answer
$a=0 \ T +2 \sqrt 2 \ N$
Work Step by Step
$v(t)=\dfrac{dr}{dt}=(\cos t -t\sin t)i+(\sin t +t\cos t )j+2t \ k $
or, $|v(t)|=\sqrt {(\cos t -t\sin t)^2+(\sin t +t\cos t )^2+(2t)^2}=\sqrt {1+5t^2}$
Now, $a(t)=\dfrac{d \ v(t)}{dt}= \dfrac{5t}{\sqrt {5t^2+1}} $
or, $|a(0)|=\dfrac{5(0)}{\sqrt {5(0)^2+1}} =\dfrac{0}{\sqrt {1}}= 0$
$a_{N}=\sqrt {|a|^2 -a^2_{T}}=\sqrt {(2\sqrt 2)^2 -0^2}=2 \sqrt 2 $
and $a=a_T T+a_{N}=0 \ T +2 \sqrt 2 \ N$
