The relation between time t and displacement x is `t = alpha x^2 + beta x,` where `alpha and beta` are constants. The retardation is

Options

A. ` 2alphav^(3)`
B. ` 2 betav^(3)`
C. `2 alphabetav^(3)`
D. `2 b^(2)v^(3)`

Answer

A

Explanation

`t alphax^(2)+betax`
Differentiating: `12alpha (dx)/(dt).x beta(dx)/(dt)`
`v=(dx)/(dt)=(1)/(beta+2alphax),(dt)/(dt) =(-2alpha v)/((beta +2 alpha x))^(2) =2 alpha v^(3)`.