Newton's laws of motion work best for objects under which conditions.

a. very slow and fast moving.
b. very large and slow moving.
c. very small and slow moving.
d. very large and fast moving.

Newton's laws of motion work best for objects under conditions (b) very large and slow moving.

To explain why, let's understand Newton's laws of motion first:

1. Newton's First Law of Motion (Law of Inertia) states that an object at rest will stay at rest, and an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an external force.

2. Newton's Second Law of Motion states that the force acting on an object is equal to the mass of the object multiplied by the acceleration of the object. It can be represented by the formula F = ma.

3. Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.

Now, considering these laws, let's analyze the given options:

a. Objects that are very slow and fast moving: In these cases, the effects of forces acting on the objects may vary significantly. High speeds or sudden changes in speed can introduce factors like air resistance, friction, and other external forces that can impact the object's motion. These additional factors can make it difficult to accurately apply Newton's laws of motion.

b. Objects that are very large and slow moving: When objects are large and moving slowly, the effects of external forces like air resistance and friction are typically minimal. In this scenario, it becomes easier to isolate and analyze the forces acting on the object, making it more suitable for applying Newton's laws of motion.

c. Objects that are very small and slow moving: Similarly, when objects are small and moving slowly, the impact of external forces can be relatively insignificant. By minimizing these effects, it becomes easier to observe and analyze the forces acting on the object, making it suitable for applying Newton's laws of motion.

d. Objects that are very large and fast moving: When objects are large and moving at high speeds, the effects of external forces like air resistance become more significant. Additionally, the impact of inertia, momentum, and other factors that arise at higher speeds can complicate the application of Newton's laws.

Considering these explanations, option (b) very large and slow moving is the most appropriate condition under which Newton's laws of motion work best for objects.