A body a starts from rest with an acceleration `a_(1)` . After 2s, 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 :

Options

A. ` 9 : 7`
B. `9 : 5`
C. `5 : 7`
D. `5 : 9`

Answer

D

Explanation

`S_(n) = u +(a)/(2) (2n-1)`
`S_(5^(th))(A) = S_(3^(th))(B)`
`0 + (a_(1))/(2) [(2 xx5)=1] = 0 +(a_(2))/(2) [ (2xx3) - 1]`
`(a_(1)xx9)/(2) = (a_(2) xx5)/(2)`
`:. (a_(1))/(a_(2)) = (5)/(9)`
`a_(1) :a_(2) = 5:9`