Kinetic Energy

The kinetic energy ( ) of a body is given by: where is the mass and is the velocity of the object. Momentum ( ) is given by: Since the momentum of both bodies is equal, we have: Substitute and in terms of momentum: Now, calculate the kinetic energy for both bodies: Thus, the ratio of their kinetic energies is:

The kinetic energy ( ) of a body is given by the formula: where is the mass and is the velocity of the body. The momentum ( ) of a body is given by: If the momentum of a body doubles, the velocity of the body also doubles (since momentum is directly proportional to velocity for constant mass). Now, if the velocity is doubled, the kinetic energy will increase by a factor of: Since is doubled, the kinetic energy becomes four times greater, as . Thus, the kinetic energy will become four times greater when the momentum is doubled.