A 0 . 5   kg block moving at a speed of 12   ms - 1 compresses a spring through a distance 30…

Given: Mass of the block $m=500 \mathrm{g}$, initial velocity of the block $u=12 \mathrm{m} {\mathrm{s}}^{-1}$, and final velocity of the block $v=\frac{u}{2}=6 \mathrm{m} {\mathrm{s}}^{-1}$.

As non-conservative forces are not acting on the system we can conserve energy.

Thus, loss in kinetic energy of block $=$ Gain in potential energy of spring

$\frac{1}{2}m{u}^2-\frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2$

$\frac{1}{2}\times 0.5\times {12}^2-\frac{1}{2}\times 0.5\times 6^2=\frac{1}{2}k\times 0.3^2$

$k=600 \mathrm{N} {\mathrm{m}}^{-1}$