Question

A body $A$ starts from rest with an acceleration $a_1$. After $2 s$ another body $B$ starts from rest with an acceleration $a_2$. If they travel equal distances in $5 s$, after the starts of $A$, the ratio $a_1: a_2$ will be equal to:

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

Answer 1

Answer: (C)

The distance covered by the body in the $n$th second of motion is
$S_n=u+\frac{a}{2}(2 n-1)$
where $u$ is initial velocity and $a$ is acceleration. Distance covered by the body $A$ in 5 th second after its start, with acceleration $a_1$, is
$\left(S_5\right)_A=0+\frac{a_1}{2}(2 \times 5-1)=\frac{9 a_1}{2}$
Time taken by second body $=5-2=3 s$
$\left(S_3\right)_B=0+\frac{a_2}{2}(2 \times 3-1)=\frac{5 a_2}{2}$
Given, $\left(S_5\right) A=\left(S_3\right)_B$
$\therefore \frac{a_1}{a_2}=\frac{5}{9}$