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

Explanation

We have the relation between time t and displacement x as
`t = alphax^(2) + betax` ,
Differentiating with respect to x, we get, `(dt)/(dx) = 2 alpha x + beta`
Now, acceleration, `a=(dv)/(dt)=d/(dt)[1/(2alphax+beta)]`
`implies (d)/(dx)[1/(2alphax +beta)].(dx)/(dt)=-(2alpha)/((2alphax+beta)^2)v=-2alpha.v^2.v=-2alphav^3`
`implies a =-2 alphav^3`