Final answer:
Both a light truck and a heavy truck moving with the same momentum require the same amount of work to stop, because the work done is related to the change in their kinetic energy and not their individual masses.
Step-by-step explanation:
To answer the question concerning whether a light truck or a heavy truck moving with the same momentum requires more work to stop, we need to understand the relationship between momentum, mass, velocity, and work. Both the light truck and heavy truck have the same momentum because momentum is the product of mass and velocity. However, to have the same momentum, the lighter truck must be moving at a higher velocity than the heavier truck.
When we consider work, we have to look at the work-energy principle which states that the work done on an object is equal to the change in its kinetic energy. Since both trucks have the same momentum, they also have the same kinetic energy if we ignore air resistance and other nonconservative forces. Thus, it will require the same amount of work to stop both trucks.
The most important point here is that the amount of nonconservative work equals the change in mechanical energy. Since kinetic energy is a form of mechanical energy and both vehicles have the same kinetic energy if they have the same momentum, the work required to bring them to a stop is the same, irrespective of their masses. Therefore, the correct answer is c. Both trucks require the same work to stop.