Answer
$v=14m/s$
Work Step by Step
According to the conservation of energy, all energy must be conserved. In this case, elastic potential energy is converted to kinetic energy. This means that $$\frac{1}{2}k\Delta x^2=\frac{1}{2}mv^2$$ Solving for velocity $v$ yields $$v=\sqrt{\frac{k\Delta x^2}{m}}=\Delta x \sqrt{\frac{k}{m}}$$ Substituting known values of $\Delta x=0.15m$, $k=1.0\times 10^4N/m$, and $m=1.2kg$ yields a final velocity of $$v=(0.15m)\sqrt{\frac{1.0\times 10^4N/m}{1.2kg}}=14m/s$$
