Are there choices that come with this question?
Answer: The correct answer is option (A).
Explanation:
Momentum of the car with 0.04 kg mass , which travelling with velocity of 2.00 m/s

Then the maximum speed of the another car in order to not to break the eggs will be same as first car:



Speed slightly more than 1 m/s will increase the momentum of second car and the eggs will break. So, from the given options the minimum speed need by the second car will be 1.42m/s.
The box is kept in motion at constant velocity by a force of F=99 N. Constant velocity means there is no acceleration, so the resultant of the forces acting on the box is zero. Apart from the force F pushing the box, there is only another force acting on it in the horizontal direction: the frictional force

which acts in the opposite direction of the motion, so in the opposite direction of F.
Therefore, since the resultant of the two forces must be zero,

so

The frictional force can be rewritten as

where

,

. Re-arranging, we can solve this equation to find

, the coefficient of dynamic friction: