Find the open interval$($s$)$ on which $r(t)=t^{3}i{t}^{4}j$ is smooth. $[1]$

The position vector vec$(r)(t)=($:$4t,3cost,3sint$:$)$ describes the path of an object moving in space.

a$.$ Find the velocity vector, speed, and acceleration vector of the object.

$[3]$

b$.$ Evaluate the velocity and acceleration vectors of the object at $t=.[2]$