The position function of a particle is given by$,$r$($t$)=2$costi$+3$sintj$.$

Find the

$($a$)($i$)$ velocity,

$($ii$)$ acceleration, and

$($iii$)$ speed

of a particle at $t=0.$

$($b$)$ Sketch the path of the particle, the velocity and acceleration vectors for the

specified value of $t.$