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 `5th` second, after the start of `A`, then the ratio `a_1 : a_2` is equal to :

Options

A. `(5)/(9)`
B. `(5)/(7)`
C. `(9)/(5)`
D. `(9)/(7)`

Answer

a

Explanation

For body A
Distance travelled in `5^(th)` second
`y=(1)/(2)a_(1)(2n-1)=(9)/(2)a_(1)[because n=5s]`
For body B, the distance travelled in `3^(rd)` second n=3s
`y=(1)/(2)a_(2)(2n-1)`
`y=(1)/(2)a_(2)(5)`
`(9)/(2)a_(1)=(5)/(2)a_(2)`
`(a_(1))/(a_(2))=(5)/(9)`