If the linear momentum of a moving object changes by two times, then its kinetic energy will change by a factor of

The relationship between kinetic energy (KE) and linear momentum (p) for an object of mass (m) is expressed by the formula KE = p²/2m. This derivation is obtained by substituting the velocity (v = p/m) from the momentum equation (p = mv) into the standard kinetic energy formula (KE = 1/2 mv²). Consequently, if the mass of the object remains constant, the kinetic energy is directly proportional to the square of its linear momentum. When the linear momentum of a moving object changes by a factor of two (doubles), the kinetic energy changes by the square of that factor, which is 2² = 4. Therefore, doubling the momentum results in the kinetic energy being quadrupled, assuming the change in momentum is driven by a change in velocity rather than mass.