The displacement of a particle moving in a straight line is given by the expression `x=At^(3)+Bt^(2)+Ct+D` in metres, where t is in seconds and A,B,C and D are constant. The ratio between the initial acceleration and initial velocity is

Options

A. `(2C)/(B)`
B. `(2B)/( C)`
C. 2C
D. `( C)/(2B)`

Explanation

Displacement of a particle moving in a straight line `(x) = At^(3) + Bt^(2) + Ct + D`
`therefore "Velocity", " " v = (dx)/(dt) = 3At^(2) + 2Bt + C`
`V_("intial") = C`
and `a = (d^(2)X)/(dt^(2))` = 6At + 2B`
`a_(intial) = 2B`
`therefore` Ratio between intial acceleration and intial velocity is `(2B)/( C)`.