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Given the position equation $x( t ) =\sin { ( t ) +2, } $ at what time(s) on $[ 0,\pi ] $ will the instantaneous velocity equal its average velocity?

$t=\pi $

$t = \cfrac {(2n+1)\cdot \pi}{2}$ where $n$ = any integer

$t=0$ and $\pi $

$t=\cfrac {\pi}{2}$