Answer
The x coordinate of the center of the circular path is $~~x = 4.00~m$
Work Step by Step
We can find the radius of the circular motion:
$a = \frac{v^2}{r}$
$r = \frac{v^2}{a}$
$r = \frac{(5.00~m/s)^2}{12.5~m/s^2}$
$r = 2.00~m$
Since the acceleration vector is directed toward the center of the circle, the center of the circle is located a distance of $2.00~m$ directly above the point $(4.00~m, 4.00~m)$
The center of the circle is located at the point $(4.00~m, 6.00~m)$
The x coordinate of the center of the circular path is $~~x = 4.00~m$
