Given K1K_{1}K1 = racmv22rac{mv^{2}}{2}racmv22.
When v is halved, we have
K2K_{2}K2 = m×(v2)22\frac{m \times \left(\frac{v}{2}\right)^2}{2}2m×(2v)2
= racK14rac{K_{1}}{4}racK14
Hence, the initial kinetic energy is quartered.
