#### Answer

We should stretch the spring a distance of 0.63 m

#### Work Step by Step

The energy stored in a spring is $\frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the stretch distance. Therefore;
$\frac{1}{2}kx^2 = 200~J$
$x^2 = \frac{(2)(200~J)}{k}$
$x = \sqrt{\frac{(2)(200~J)}{k}}$
$x = \sqrt{\frac{(2)(200~J)}{1000~N/m}}$
$x = 0.63~m$
We should stretch the spring a distance of 0.63 m.