Q 11-02-025JEE MainHard
Car A starts from rest with uniform acceleration $a_1$. Three seconds later, car B starts from rest from the same point with uniform acceleration $a_2$. If the displacement of A in its $6^{\text{th}}$ second equals the displacement of B in the same interval of time, then $a_1 : a_2$ is
Answer: (B) $5 : 11$
Concept. From rest, distance in the $n$th second is $\dfrac{a}{2}(2n - 1)$. A's $6^{\text{th}}$ second ($t = 5$ to $6$ s) is B's $3^{\text{rd}}$ second.
Step 1. Equate.
$$\frac{a_1}{2}(11) = \frac{a_2}{2}(5) \;\Rightarrow\; 11a_1 = 5a_2$$
Step 2. Ratio. $a_1 : a_2 = 5 : 11$.
Answer. $5 : 11$ (Option B).
Solution by Sreeraj P, M.Sc Physics