Question

A body $A$ starts from rest with an acceleration $a_A$. After 2 seconds, another body $B$ starts from rest with an acceleration $a_B$. If they travel equal distances in the $5^{th}$ second, after the start of $A$, then the ratio $a_A:a_B$ is equal to

• A. $5:9$
• B. $5:7$
• C. $9:5$
• D. $9:7$

Answer 1

The correct option is A $5:9$

A body with initial velocity u and uniform acceleration $a$ travels distance,
$s_n=u+\frac{a}{2}(2n-1)$, in the $n^{th}$ second.
The distance travelled by $A$ in the $5^{th}$ second is
$s_{A,5^{th}}=\frac{a_A}{2}(2\times 5-1)$.
The body $B$ starts 2 seconds after start of $A$.
Thus, distance travelled by $B$ in the $3^{rd}$ second = distance travelled by $A$ in the $5^{th}$ second
$s_{B{.3}^{rd}}=\frac{a_B}{2}(2\times 3-1)$
$s_{A,5^{th}}=s_{B,3^{rd}}$
$\frac{a_A}{2}(2\times 5-1)=\frac{a_B}{2}(2\times 3-1)$
$a_A/a_B=5/9$