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

Distance travelled by body A in 5th sec
= distance travelled by body B in 3rd sec
` rArr 0 + (a_1)/(2) (2 xx 5 - 1) = 0 + (a_2)/(2) (2 xx 3 - 1)`
`rArr 9a_1 = 5a_2 rArr a_1/a_2 = 5/9`