The acceleration (a) of moving particle varies with displacement according to the following relation ` a = X^(2)+3X`, Then correct relation between velocity and displacement is :-

Options

A. `V=sqrt((X^(2))/(3)+(3X^(2))/(2)+C)`
B. `V=sqrt((2)/(3)X^(3)+3X^(2)+C)`
C. `V=((2)/(3)X^(3)+3X^(2)+C)`
D. `V = 2x + 3`

Answer

C

Explanation

`vec(a)=(dvec(v))/(dt)` is negative, but `vec(v)` = positive implies `vec(a)` and `vec(v)` are in opposite direction