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 :

Options

A. 0.21458333333333
B. 0.21319444444444
C. 0.37847222222222
D. 0.37986111111111

Answer

A

Explanation

Time taken by body A, `t_1 = 5 s `
Acceleration of body A = `a_1`
Time taken of body B, `t_2 = 5 - 2 = 3 s`
Acceleration of body `B = a_2`
Distance covered by first body in `5^(th)` second after its start,
`S_5 = u + a_1/2(2t_1 - 1)` = `0 + a_1/2 (2 xx 5 - 1)` = `9/2 a_1`
Distance covered by the second body in the `3^(rd)` second after its start,
`S_3 = u + a_2/2(2t_2 - 1) = 0 + a_2/2(2 xx 3 -1) = 5/2 a_2`
Since `S_5 = S_3 therefore 9/2 a_1 = 5/2 a_2` or `a_1 : a_2 = 5 : 9`