An object is subjected to an acceleration `a = 4 + 3v`. It is given that the displacement `S = 0` when `v = 0`. The value of displacement when `v = 3 m//s` is

Options

A. `1 + (4)/(3) ln((13)/(4))`
B. `1 - (4)/(3)ln ((13)/(8))`
C. `1 - (4)/(9) ln ((13)/(4))`
D. `1 + (4)/(9) ln ((13)/(8))`

Answer

C

Explanation

`a = v (dv)/(dS) = 4 + 3v`
`underset(0)overset(v)int (vdv)/(4 + 3v) = underset(0)overset(S)int dS`
`S = 1 - (4)/(9)l ((13)/(4))`