$(4$ points each$)$ Let $r(t)=($:$2cost,2sint,2t$:$).$

$($a$)$ Compute $v(t)$ and $a(t).$

$($b$)$ Use the formula $a_T=\frac{d}{dt}|v|$ to find the tangential component of acceleration.

$($c$)$ Use the formula $a_N=\sqrt[\phantom{2}]{|a{|}^2-a_T^2}$ to find the normal component of acceleration.