Write down the total momentum for two marbles of mass, m, both moving at velocity, v. What is the kinetic energy of the system.

The momentum of marble-A is (m v).

The momentum of marble-B is (m v)

Momentum is a vector quantity, and we don't know the direction

either marble is moving. So we don't know how their momenta

will combine. The sum of their momenta is something between

zero and (2mv).

The kinetic energy of marble-A is (1/2 m v²).

The kinetic energy of marble-B is (1/2 m v²).

If the marbles are the only matter in the system, then

the total kinetic energy in the system is (m v²).

Mv + mv = 2mv providing each momentum is in the same direction.

1/2 mv^2 + 1/2 mv^2 = mv^2