Question

$A$ starts from rest and moves with an 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 accelerations $a_1$ and $a_2$ are

• A. $2m/s^2,35m/s^2$
• B. $5m/s^2,9m/s^2$
• C. $11m/s^2,2m/s^2$
• D. $1m/s^2,10m/s^2$

Answer 1

Answer: (B)

$5m/s^2,9m/s^2$

By using: $S_n=u+\frac{a}{2}(2n-1)$
Distance travelled by body $A$ in $5^{th}$ second $=0+\frac{a_1}{2}(2\times 5-1)$
Distance travelled by body $B$ in $3^{rd}$ second is $=0+\frac{a_2}{2}(2\times 3-1)$ since B started 2 seconds after A started.
According to problem : $0+\frac{a_1}{2}(2\times 5-1)=0+\frac{a_2}{2}(2\times 3-1)$
$\Rightarrow 9a_1=5a_2\Rightarrow \frac{a_1}{a_2}=\frac{5}{9}$
Option(B) only has the correct ratio.