#### Answer

$k = 2.0~m/s^3$

#### Work Step by Step

$x(t) = x_0+\int_{0}^{t}~v(t)~dt$
$x(t) = x_0+\int_{0}^{t}~kt^2~dt$
$x(t) = \frac{k}{3}t^3-9.0$
At t = 3.0 s;
$\frac{k}{3}t^3-9.0~m = 9.0~m$
$\frac{k}{3}(3.0~s)^3-9.0~m = 9.0~m$
$(9.0~s^3)~k = 18.0~m$
$k = 2.0~m/s^3$