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 $5^{\text{th}}\text{second}$ 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 $5:9$

According to problem
Distance travelled by body $A$ in $5^{\text{th}}\text{sec}$ 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 $S_{5^{th}}=S_{3^{rd}}$
$\Rightarrow 0+\frac{a_1}{2}(2\times 5-1)=0+\frac{a_2}{2}(2\times 3-1)$
$9a_1=5a_2\Rightarrow \frac{a_1}{a_2}=\frac{5}{9}$