Distance And Displacement

To solve this problem, we need to understand the motion of a block sliding down a smooth inclined plane. Since the inclined plane is smooth, there is no friction acting on the block, and it is under the influence of gravity. This scenario is a classic example of uniformly accelerated motion.

The block starts from rest, so its initial velocity . Let be the acceleration of the block due to gravity along the inclined plane. The distance traveled by the block in the time interval to is given by the equation of motion:

Since the initial velocity , this simplifies to:

Now, let's calculate the distances and for the successive intervals:

The distance traveled in the interval from to is:

Similarly, the distance traveled in the interval from to is:

Now, we find the ratio:

This matches the correct answer:

Option: