Question $3(15$pts$)$: An observer, after observing the motion of a flying bird for $30$ minutes, using the Cartesian

coordinate data where the origin is taken as the position of the observer, he finds the following equaitons for the

coordinates of the bird: $=2$

$2+5,=4$

$22+2,$ and $=3+8.$

$($a$)$ Calculate the average velocity vector of the bird between $=2$ and $=8$ seconds.

$($b$)$ What was the velocity of the bird at $=6$ s $?$

$($c$)$ What was the acceleration $($vector$)$ at t $=6$ seconds?