Final answer:
Two particles with equal momentum do not always have equal kinetic energies unless their masses are equal. In the described collision scenario, momentum is conserved, but kinetic energy is not necessarily conserved, indicating an inelastic collision.
Step-by-step explanation:
If two particles have equal momentum, their kinetic energies are not necessarily equal. The kinetic energy of an object can be calculated using the formula KE = (1/2)m·v^2, where m is mass and v is velocity. However, momentum is calculated using the formula p = m·v. So, for two particles with equal momentum, it's possible for their kinetic energies to be unequal if their masses or velocities differ. Specifically, the kinetic energy depends on the square of the velocity, meaning that an object with a higher velocity but equal mass to another object will have greater kinetic energy. The correct answer to the student's question is: (c) no, except when their masses are equal.
In the scenario where two objects of equal mass collide, with Object A initially moving and Object B initially at rest, and following the collision Object A is at rest and Object B is moving away with some unknown velocity, the statement we can make about this collision is that momentum is conserved, but kinetic energy is not necessarily conserved. This is typically characteristic of an inelastic collision, where the objects do not rebound off each other perfectly. The correct answer is (b) Momentum is conserved, but kinetic energy is not conserved.