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. `2 alpha v^3`
B. `2 beta v^3`
C. `2 alpha beta v^3`
D. `2 beta^2 v^3`

Answer

A

Explanation

`(dt)/(dx)=(2 alphax+beta)`
`:. (dx)/(dt)=v=(1/(2 alphax+beta))`
`a=(dv)/(dt)=-2 alpha(1/(2 alphax+beta))^2.(dx)/(dt)`
`=-2alpha(v)^2(v)=-2 alpha(v)^3`