## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

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