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 $5^{th}$ 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

$5:9$

Given,

Initial speed $u=0$

We know,

Distance covered in nth second after starting from rest $S=\frac{1}{2}(2n-1)$

Now,

For A : $n=5$

So, $S_A=\frac{a_1}{2}(2\times 5-1)=\frac{9}{2}{a}_1$

SInce B starts after 2 second of A So,

For B : $n=3$

So, $S_B=\frac{a_2}{2}(2\times 3-1)=\frac{5}{2}{a}_2$

But according to question distance travelled is equal so, $S_A=S_B$

Or, $\frac{9}{2}{a}_1=\frac{5}{2}{a}_2$

After solving $⟹a_1:a_2=5:9$

Hence, ratio is 5 : 9