The law of motion that applies to the statement "It is difficult to move fast when you carry a heavy bag" is primarily related to inertia and acceleration.
The law of inertia, which is Newton's first law of motion, states that an object at rest will remain at rest, and an object in motion will continue moving at a constant velocity unless acted upon by an external force. In this case, the heavy bag represents an additional mass that you need to overcome with an external force to set it in motion or change its velocity.
When you carry a heavy bag, it increases the total mass of your body-bag system. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Mathematically, this can be expressed as F = ma, where F represents the net force, m represents the mass, and a represents the acceleration.
Applying this law to the scenario, when you carry a heavy bag, the increased mass (m) requires a larger force (F) to accelerate the system. Since you need to exert more force to overcome the bag's mass, it becomes difficult to move fast. The bag adds an additional resistance to your motion due to its mass, requiring more force and effort to accelerate the combined system.
In summary, the difficulty in moving fast while carrying a heavy bag is due to the increased mass of the system, which requires more force and effort to accelerate as stated by Newton's second law of motion.