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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
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The correct answer is:
5:9
According to problem
Distance travelled by body $A$ in $5^{\text {th }} \sec$ and distance travelled by body $B$ in $3^{\text {rd }}$ sec of its motion are equal.
$\begin{aligned} & 0+\frac{a_1}{2}(2 \times 5-1)=0+\frac{a_2}{2}[2 \times 3-1] \\ & 9 a_1=5 a_2 \Rightarrow \frac{a_1}{a_2}=\frac{5}{9}\end{aligned}$
Distance travelled by body $A$ in $5^{\text {th }} \sec$ and distance travelled by body $B$ in $3^{\text {rd }}$ sec of its motion are equal.
$\begin{aligned} & 0+\frac{a_1}{2}(2 \times 5-1)=0+\frac{a_2}{2}[2 \times 3-1] \\ & 9 a_1=5 a_2 \Rightarrow \frac{a_1}{a_2}=\frac{5}{9}\end{aligned}$
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