AIIMS 2019 Physics Equations of Motion MCQ Question

In this problem, we analyze the distances traveled by both bodies A and B during the fifth second of their motion. Body A, which starts first, covers a distance given by $S_A = \frac{1}{2} a_1 (t + 2)^2 - \frac{1}{2} a_1 (t + 1)^2$ for the fifth second, while body B, starting two seconds later, covers $S_B = \frac{1}{2} a_2 (t + 1)^2 - \frac{1}{2} a_2 t^2$. Setting these distances equal for the fifth second and simplifying leads to the ratio $\frac{a_1}{a_2} = \frac{5}{9}$, confirming option C as correct. Other options are incorrect as they do not satisfy the derived relationship between the accelerations based on the equal distances traveled in the specified time frame.