## University Physics with Modern Physics (14th Edition)

The kinetic energy of the box will be equal to the elastic potential energy stored in the spring. $\frac{1}{2}mv^2 = \frac{1}{2}kx^2$ $x^2 = \frac{mv^2}{k}$ $x = v~\sqrt{\frac{m}{k}}$ $x = (3.0~m/s)~\sqrt{\frac{6.0~kg}{7500~N/m}}$ $x = 0.085~m$ The maximum compression of the spring is 0.085 meters.