Question

A body starts from rest with an acceleration $a_1$. After two seconds another body $B$ starts from rest with an acceleration $a_2$. If they travel equal distances in fifth second 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)

$5:9$

Distance travelled in fifth second for first body = distance travelled in 3rd second for second body,

$S_5=S_3$

$S_t=u+\frac{(2t-1)a}{2}$

$S_5=0+\frac{9}{2}{a}_1$

$S_3=0+\frac{5}{2}{a}_2$

$\frac{9}{2}{a}_1=\frac{5}{2}{a}_2\Rightarrow \frac{a_1}{a_2}=\frac{5}{9}$