question_answer

A body A starts from rest with an acceleration \[{{a}_{1}}\]After two seconds, another body B starts from rest with an acceleration\[{{a}_{2}}\]. If they travel equal distance in the 5th second after the start of A, then find the ratio\[{{a}_{1}}:{{a}_{2}}\].

Answer:

Distance travelled by A in5th second, \[{{S}_{A}}=0+\frac{{{a}_{1}}}{2}(2\times 5-1)=\frac{9}{2}{{a}_{1}}\]                        ….(1) Distance travelled by B in 3rd second, \[{{S}_{B}}=0+\frac{{{a}_{2}}}{2}(2\times 3-1)=\frac{5}{2}{{a}_{2}}\] Given,\[{{S}_{A}}={{S}_{B}}\] \[\frac{9}{2}{{a}_{a}}=\frac{5}{2}{{a}_{2}}\,\,or\,\,\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{5}{9}\]