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 $A$, $t_1 = 5 \,s$
Acceleration of body $A = a_1$
Time taken by body $B$, $t_2 = 5 - 2 = 3\,s$
Acceleration of body $B = a_2$
Distance covered by first body in $5^{th}$ second after its start,
$S_{5}=u+\frac{a_{1}}{2}\left(2t_{1}-1\right)$
$=0+\frac{a_{1}}{2}\left(2\times5-1\right)=\frac{9}{2} a_{1}$
Distance covered by the second body in the $3^{rd}$ second after its start,
$S_{3}=u+\frac{a_{2}}{2}\left(2t_{2}-1\right)$
$=0+\frac{a_{2}}{2}\left(2\times3-1\right)=\frac{5}{2} a_{2}$
Since $S_{5}=S_{3}$
$\therefore \frac{9}{2}a_{1}=\frac{5}{2}a_{2}$ or $a_{1} : a_{2}=5 : 9$