Question

A starts from rest and moves with acceleration $a_1$. Two seconds later, B starts from rest and moves with an acceleration $a_2$. If the displacement of A in the $5^{th}$ second is the same as that of B in the same interval, the ratio of $a_1$ to $a_2$ is

• A. $9:5$
• B. $5:9$
• C. $1:1$
• D. $1:3$

Answer 1

The correct option is B $5:9$

Displacement of A in $5^{th}$ sec:
$A\Rightarrow s_5-s_4=\frac{1}{2}\times a_1(5{)}^2-\frac{1}{2}{a}_1(4{)}^2=\frac{1}{2}{a}_1\times 9$

Displacement of B in $5^{th}$ sec is displacement in $3^{rd}$ sec of journey for B:
$B\Rightarrow s_3-s_2=\frac{1}{2}{a}_2(3{)}^2-\frac{1}{2}{a}_2(2{)}^2=\frac{1}{2}{a}_2\times 5$

So Displacements,
$\therefore \frac{A}{B}=\frac{\frac{1}{2}{a}_1\times 9}{\frac{1}{2}{a}_2\times 5}\Rightarrow \frac{a_1}{a_2}=\frac{5}{9}$