The position vector r describes the path of an object moving in space.

Position Vector$$Time

r$($t$)=$ t$2$i $+$ tj $+2$t$3/2$k

t $=4$

$($a$)$ Find the velocity vector v$($t$),$ speed s$($t$),$ and acceleration vector a$($t$)$ of the object.

v$($t$)=$

s$($t$)=$

a$($t$)=$

$($b$)$ Evaluate the velocity vector and acceleration vector of the object at the given value of t$.$

v$(4)=$

a$(4)=$