Answer
$a=0 \ T +2 \sqrt 2 \ N$
Work Step by Step
We calculate the velocity and acceleration as follows:
$v(t)=\dfrac{dr}{dt}=(\cos t -t\sin t)i+(\sin t +t\cos t )j+2t \ k \implies |v(t)|=\sqrt {(\cos t -t\sin t)^2+(\sin t +t\cos t )^2+(2t)^2}=\sqrt {5t^2+1}$
and $a(t)=\dfrac{d \ v(t)}{dt}= \dfrac{5t}{\sqrt {5t^2+1}} $
$|a(0)|=\dfrac{5(0)}{\sqrt {5(0)^2+1}} = 0$
Now, $a_{N}=\sqrt {|a|^2 -a^2_{T}}=\sqrt {(2\sqrt 2)^2 -(0)^2}=2 \sqrt 2 $
So, $a=a_T T+a_{N}=0 \ T +2 \sqrt 2 \ N$
