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 5th 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

Answer: (A)

Time taken by body $A$, $t_1=5s$
Acceleration of body $A=a_1$
Time taken by body $B$, $t_2=5-2=3s$
Acceleration of body $B=a_2$
Distance covered by first body in $5^{th}$ second after its start,
$S_5=u+\frac{a_1}{2}\left(2t_1-1\right)$
$=0+\frac{a_1}{2}\left(2\times 5-1\right)=\frac{9}{2}{a}_1$
Distance covered by the second body in the $3^{rd}$ second after its start,
$S_3=u+\frac{a_2}{2}\left(2t_2-1\right)$
$=0+\frac{a_2}{2}\left(2\times 3-1\right)=\frac{5}{2}{a}_2$
Since $S_5=S_3$
$\therefore \frac{9}{2}{a}_1=\frac{5}{2}{a}_2$ or $a_1:a_2=5:9$