To find the ratio of distances traveled in each 2-second interval, we use the equations of motion under

constant acceleration. The particle starts from rest, so the initial velocity . The distance traveled in time under constant acceleration is given by .
Step 1
In the first 2 seconds, the distance traveled is given by:

Step 2
In the first 4 seconds, the total distance traveled is given by:

Step 3
So, the distance traveled in the second interval of 2 seconds is:

Step 4
In the first 6 seconds, the total distance traveled is given by:

Step 5
So, the distance traveled in the third interval of 2 seconds is:

The ratio is , which simplifies to . Therefore, the correct option is 3 .