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