$(48\mathrm{.}1)$ A rigid body rotating about a fixed axis has its angular position $($in degrees$)$ recorded at the times shown in the chart.

$\backslash$table$[[$Time $[$s$],0,1,2,3],[$Position $[],30,70,120,180]]$

$($a$)$ Determine the average angular velocity of the rotating body during the time intervals:

$($i$)$ tin$[0,2],{}_{av,i}=$

$($ii$)$ tin$[1,3],{}_{av,iv}=$

$($iii$),$tin$[0,3],{}_{av,\text{i}\text{t}\text{i}}=$

$(18\mathrm{.}2)$ A rigid body rotating about a fixed axis has its angular position described by

$(t)=2t^3+3t^2$

where $$ is in radians and $t$ is in scconds.

$($a$)($i$)$ Determine the angular position of the body at $t=2s$ and at $t=4s.$

$($ii$)$ Compute the average angular velocity of the body during the time interval from $t=2s$ to $t=4s.$

$($b$)$ Determine an expression for the instantaneous angular velocity of the rotating body.

$($c$)($i$)$ Determine the angular velocity of the body at $t=2s$ and at $t=4s.$

$($ii$)$ Compute the average angular acceleration of the body during the time interval from $t=2s$ to $t=4s.$

$($d$)$ Determine an expression for the instantaneous angular acceleration of the rotating body.