A body" A " starts from rest with an acceleration $a_1$.  After 2 sec, another body" B " starts from rest with an acceleration $a_2$.  If they cover equal distances in the 5th second after the start of A, then the ratio of $a_1:a_2$  is equal to 

 $$\begin{gathered} given initial velocity u=0;acceleration =a_1;time n=5sec;substitute in, \\ {S}_n=u+\frac{a}{2}(2n-1)---\left(1\right)x \\ body A:S=0+\frac{1}{2}{a}_1(2\times 5-1)=\frac{9a_1}{2}\text{---(3)} \\ \text{body B:→}given initial velocity u=0;acceleration =a_2;time n=3sec;substitute in equation\left(1\right) \\ S=0+\frac{1}{2}{a}_2(2\times 3-1)=\frac{5a_2}{2}\text{---(4)} \\ equate equations \left(3\right) and \left(4\right) \\ \hspace{0.17em}\hspace{0.17em}\frac{9a_1}{2}=\frac{5a_2}{2} \\ \text{⇒}\hspace{0.17em}\frac{a_1}{a_2}=\frac{5}{9} \end{gathered}$$