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. ` 2alpha betav ^(3) `
D. ` 2 beta ^(2) v^(3) `

Answer

A

Explanation

` (dt)/( dx) =2alpha x+beta rArr v = (1)/( 2alpha x+beta ) " "because " "a=( dv)/(dt) =(dv)/(dx) .(dx)/(dt) `
` a=v (dv)/(dx) =( -v.2alpha )/((2alpha x +beta)^(2)) =-2alpha v.v^(2) =-2alpha v^(3) " "therefore " " ` Retardation =`2alpha v^(3)`