Answer
The work done on the brick by the force is $~~800~J$
Work Step by Step
We can write an expression for the acceleration at $x$:
$a = 2.5~x$
We can write an expression for $F$:
$F = ma$
$F = 2.5~mx$
$F = 25x$
We can find the work done on the brick by the force:
$W = \int^{8.0}_{0}25x~dx$
$W = 12.5x^2~\Big\vert^{8.0}_{0}$
$W = (12.5)(8.0)^2-(12.5)(0)^2$
$W = 800~J$
The work done on the brick by the force is $~~800~J$
