$If$ the vector function vec$(r)(t)=($:$cos(t),sin(t),t^2-3t$:$)$ models the position $of$ a particle, what $is$ the velocity vector $of$

the particle?

vec$(v)(t)=($:$,$:$)$

What $is$ the distance the particle travels from $t=0tot=5?$ Round your answer $to3$ decimal places.

$d=$