Question

A body A starts from rest with an acceleration $a_1$. After 2 seconds, another body B starts from rest with an acceleration $a_2$. If they travel equal distances in the $5^{th}$ second, after the start of A, then the ratio $a_1:a_2$ is equal to

• A. 5 : 9
• B. 5 : 7
• C. 9 : 5
• D. 9 : 7

Answer 1

The correct option is A 5 : 9

By using $S_n=u+\frac{a}{2}(2n-1),$ Distance travelled by body A in $5^{th}$ second $=0+\frac{a_1}{2}(2\times 5-1)$
Distance travelled by body B in $3^{rd}$ second is $=0+\frac{a_2}{2}(2\times 3-1)$
According to problem: $0+\frac{a_1}{2}(2\times 5-1)=0+\frac{a_2}{2}(2\times 3-1)\Rightarrow 9a_1=5a_2\Rightarrow \frac{a_1}{a_2}=\frac{5}{9}$