Two objects are mocing about so that their total momentum is zero. What can be said about their kinetic energy? Choose the most descriptive answer.

a. the kinetic energy must be greater than zero

b. the kinetic energy must be negative

c. the kinetic energy must be equal to or greater than zero

d. the kinetic energy is zero

e. nothing can be known about the kinetic energy

To determine the answer to this question, we need to understand the relationship between momentum and kinetic energy.

Momentum is a vector quantity that depends on both an object's mass and velocity. It is calculated by multiplying an object's mass by its velocity. On the other hand, kinetic energy is a scalar quantity that depends on an object's mass and velocity as well but is calculated using a different formula: Kinetic energy = (1/2) × mass × velocity^2.

Given that the total momentum of the two objects is zero, it means that their momenta are equal but opposite in direction, canceling each other out. Mathematically, we can express this as:
m₁v₁ + m₂v₂ = 0

Now, let's consider the possibilities:

a. The kinetic energy must be greater than zero: This statement is not accurate because there is no information that guarantees the kinetic energy to be greater than zero. Therefore, it is not the most descriptive answer.

b. The kinetic energy must be negative: This statement is also incorrect. Kinetic energy is always a positive value as it represents the energy of an object in motion. Thus, it cannot be negative.

c. The kinetic energy must be equal to or greater than zero: This statement is a valid description. Since kinetic energy is always positive, it implies that the kinetic energy must be equal to or greater than zero. However, this is not the most precise answer.

d. The kinetic energy is zero: In this scenario, both objects have a velocity of zero. Consequently, the kinetic energy of both objects is zero since kinetic energy depends on the square of the velocity. Therefore, this is the most accurate answer.

e. Nothing can be known about the kinetic energy: This statement is not accurate. Although there is no information about the specific velocities or masses of the objects, from the fact that the total momentum is zero, we can deduce that the kinetic energy is also zero.

Therefore, the correct and the most descriptive answer is d. The kinetic energy is zero.