Answer
a. Yes.
b. No.
c. Yes.
Work Step by Step
a. If a single point object has zero momentum $m\vec{v}$, either the mass or the velocity is zero, i.e., it must be stationary. In that case it has zero kinetic energy $\frac{1}{2}mv^2$.
b. Momentum is a vector, so 2 moving objects can have equal and opposite momentum vectors that sum to zero. For example, consider 2 identical objects, one moving east and one moving west at the same speed. Because they are moving, each has nonzero kinetic energy. Kinetic energy cannot be negative, so the total kinetic energy is nonzero.
c. Kinetic energy cannot be negative. Each object must have zero kinetic energy. If a single point object has zero kinetic energy $\frac{1}{2}mv^2$, either the mass or the velocity is zero, i.e., it must be stationary. Both particles are stationary, and stationary objects have zero momentum.
