Answer
$x = 4.7~m$
Work Step by Step
We can find the kinetic energy at $x=3.0~m$:
$K = \frac{1}{2}mv^2$
$K = \frac{1}{2}(2.0~kg)(8.0~m/s)^2$
$K = 64~J$
We can find the kinetic energy at $x$:
$K = \frac{1}{2}mv^2$
$K = \frac{1}{2}(2.0~kg)(5.0~m/s)^2$
$K = 25~J$
We can find the work done on the block by the force $F_x$:
$64~J+W = 25~J$
$W = 25~J-64~J$
$W = -39~J$
We can use the work done on the block by the force to find $x$:
$W = \int^{x}_{3.0}-6x~dx$
$W = -3x^2~\Big\vert^{x}_{3.0}$
$W = -3x^2-[(-3)(3.0)^2]$
$W = -3x^2+27$
$3x^2 = 27-(-39)$
$3x^2 = 66$
$x^2 = 22$
$x = \sqrt{22}$
$x = 4.7~m$
