Final answer:
When a marble is replaced by a solid cylinder on an incline, the solid cylinder will have a smaller acceleration due to its greater moment of inertia, resulting in the cylinder traveling a greater distance in the same time if starting from rest.
Step-by-step explanation:
When replacing a marble with a solid cylinder for a physics problem involving rolling down an incline, the moment of inertia involved in the calculation changes. Because a solid cylinder has a different distribution of mass, its moment of inertia is 1/2 MR2 where M is the mass and R is the radius. A marble, modeled as a solid sphere, has a moment of inertia of 2/5 MR2. The difference in the moment of inertia means that the solid cylinder will have a different acceleration than the marble.
The acceleration of a rolling object is determined by the force of gravity, friction, and the object's moment of inertia. Using the parallel axis theorem and conservation of energy, the acceleration of the solid cylinder will be less than that of a marble, because for rolling objects the acceleration a = gsin(theta) / (1+ I/(MR2)), where I is the moment of inertia and theta is the angle of inclination. Since the cylinder's I/MR2 ratio is larger, the denominator is larger, and thus the acceleration is smaller.
Hence, for a solid cylinder, the acceleration decreases but it will roll a greater distance in the same time span if the incline and surface conditions remain unchanged, because it starts from rest and has smaller acceleration over the course of 3 seconds. Therefore, the answer is (c) The acceleration decreases; distance traveled increases.