Question

A body $A$ starts from rest with an acceleration $a_1$ . After $3$ seconds, another body $B$ starts from rest with an acceleration $a_2$ . If they travel equal distances in the $6^{\text{th}}\text{second}$ after the start of $A$, then the ratio $a_1:a_2$ is equal to

• A. $5:9$
• B. $3:5$
• C. $5:11$
• D. $5:7$

Answer 1

The correct option is C $5:11$

According to problem
Distance travelled by body $A$ in $6^{\text{th}}\text{sec}$ and distance travelled by body $B$ in $3^{\text{rd}}\text{sec}$. of its motion are equal.
As we know that the distance travelled by the particle in $n^{th}$ sec is given as
$S_n=u+\frac{a}{2}(2n-1)$
Thus, we have $S_{6^{th}}=S_{3^{rd}}$
$\Rightarrow 0+\frac{a_1}{2}(2\times 6-1)=0+\frac{a_2}{2}(2\times 3-1)$
$\Rightarrow 11a_1=5a_2\Rightarrow \frac{a_1}{a_2}=\frac{5}{11}$