(Solved): A coyote notices a rat running past it, toward a bush where the rat will be safe. The rat is running ...

A coyote notices a rat running past it, toward a bush where the rat will be safe. The rat is running with a constant velocity of $v_{\text{rat }}=5\mathrm{m}/\mathrm{s}$ and the coyote is at rest, $?x=22\mathrm{m}$ to the left of the rat. However, at $t=0\mathrm{s}$, the coyote begins running to the right, in pursuit of the rat, with an acceleration of $a_{\text{coyote }}=6\mathrm{m}/{\mathrm{s}}^2$. Set your reference frame to be located with the origin at the original location of the coyote and the rightward direction corresponding to the positive $x$-direction. Write the position of the rat as a function of time $x_{\text{rat }}(t)$. Do not plug in numerical values for this part. Use the following table as a reference for each variable. Note that it may not be necessary to use every variable. What is the location at which the coyote will catch the rat $x_{\text{coyote }}\left(t_{\text{catch }}\right)=x_{\text{rat }}\left(t_{\text{catch }}\right)$ ? $x_{\text{coyote }}\left(t_{\text{catch }}\right)=x_{\text{rat }}\left(t_{\text{catch }}\right)=$