Evaluate the following two statements concerning a system of...

The kinetic energy of a system of particles is given by $K = \sum \dfrac{1}{2} m_i v_i^2$.

If the kinetic energy of the system is zero, i.e., $K = 0$, then $v_i = 0$ for all particles since the kinetic energy of individual particles cannot be negative.

If all particles are at rest, the linear momentum of the system $\vec{P} = \sum m_i \vec{v}_i$ must also be zero. Thus, statement B implies statement A.

The linear momentum of a system is given by $\vec{P} = \sum m_i \vec{v}_i$.

If the linear momentum of the system is zero, it is possible that individual particles are moving such that their vector sum of momenta is zero (for example, two particles of equal mass moving with equal speeds in opposite directions). In this case, the kinetic energy of the system will be non-zero.

Thus, statement A does not imply statement B.