Answer
The maximum kinetic energy is $~~18.0~J$
Work Step by Step
The kinetic energy continues increasing as long as the work done by the force is positive. After the body passes $x = 1.0~m$, the force is negative. Thus, work done by the force is negative and the kinetic energy of the body will begin to decrease.
The kinetic energy reaches a maximum at $x = 1.0~m$
To calculate the work done by the force between $x = 0$ and $x =1.0~m$, we can find the area under the force versus position graph:
$A = \frac{1}{2}(4.0~N)(1.0~m) = 2.0~J$
We can find the initial kinetic energy at $x = 0$:
$K_i = \frac{1}{2}mv^2$
$K_i = \frac{1}{2}(2.0~kg)(4.0~m/s)^2$
$K_i = 16.0~J$
We can find the kinetic energy at $x = 1.0~m$:
$K_f-K_i = W$
$K_f = K_i+W$
$K_f = 16.0~J+2.0~J$
$K_f = 18.0~J$
The maximum kinetic energy is $~~18.0~J$.
