Consider the following position function.

r$($t$)=$

t$4+2,$ t$5,$ t$42$

$($a$)$ Find the velocity of a particle with the given position function.

v$($t$)=$

$($b$)$ Find the acceleration of a particle with the given position function.

a$($t$)=$

$($c$)$ Find the speed of a particle with the given position function.

$|$v$($t$)|=$