Two objects, x, and y have equal mass and are moving with speeds u and 3u respectively. Their kinetic energies kx and ky are related as

The kinetic energy (KE) of an object is defined as the energy it possesses due to its motion, calculated using the formula KE = 1/2 mv², where 'm' is mass and 'v' is velocity. Since both objects x and y have equal mass, their kinetic energies depend solely on the square of their respective speeds. For object x with speed u, the kinetic energy kx is proportional to u². For object y with speed 3u, the kinetic energy ky is proportional to (3u)², which equals 9u². Consequently, the kinetic energy of object y is nine times that of object x (ky = 9kx). This relationship demonstrates that while kinetic energy is directly proportional to mass, it is proportional to the square of the velocity, meaning a tripling of speed results in a ninefold increase in energy.