Question

By what factor does the kinetic energy of a moving body change, when its speed is reduced by half?

Answer 1

Kinetic energy is given by

\[ K = \frac{1}{2}mv^{2} \]

If the speed is halved,

\[ v' = \frac{v}{2} \]

then

\[ K' = \frac{1}{2}m\left(\frac{v}{2}\right)^{2} \]

\[ = \frac{1}{4}\left(\frac{1}{2}mv^{2}\right) \]

\[ = \frac{K}{4} \]

Thus, the kinetic energy becomes one-fourth of its original value (a fourfold decrease).