Answer: Option C.
Explanation:
When the box is moving, he pushes with a force F.
in this case, the coefficient is μk, and the box is accelerating, this means that the net force is not zero, so F is larger than the friction force.
When the box is still, the man pushes again with a force F, but now the box does not move, so there is no acceleration, which means that the net force is zero, then F is not greater than the maximum static friction force.
Now, the friction force between an object of mass M, and a surface with a coefficient of friction μ is: μ*m*g
where g is the gravitational acceleration.
Then, from the first part, we can conclude that:
μk*m*g < F
(the force F is larger than the kinetic friction force)
and from the second part, we know that:
F ≤ μs*m*g
(The force F is not greater than the static friction force)
If we write those two together, we have:
μk*m*g < F ≤ μs*m*g
Then the correct option is c.
