If two particles have equal momenta, which of the following statements must be true? ($p=mv$)

• A. They have the same magnitude of velocity if their masses are equal. ($m=m\to v=v$)
• B. They must have the same mass. ($m=m$)
• C. They must be moving in the same direction.
• D. They must have the same kinetic energy. ($E=\frac{1}{2}m{v}^2$)

Answer: (A)

Verified step by step guidance

1. Recall the definition of momentum: \(p = m \times v\), where \(m\) is mass and \(v\) is velocity.
2. If two particles have equal momenta, then \(m_1 v_1 = m_2 v_2\).
3. Analyze the case when the masses are equal (\(m_1 = m_2\)). In this case, the equation simplifies to \(v_1 = v_2\), meaning the particles have the same magnitude of velocity.
4. Consider whether the particles must have the same mass: equal momentum does not imply equal mass, because velocity can vary to compensate.
5. Evaluate if the particles must have the same kinetic energy: since kinetic energy is \(E = \frac{1}{2} m v^2\), equal momentum does not guarantee equal kinetic energy because kinetic energy depends on the square of velocity and mass separately.