The relation between time and distance is t = αx2+βx, where α and β are constants. The retardation is
2αv3
2βv3
2αβv3
2β2v3
dtdx = 2αx + β ⇒ v = 12αx+β
∴ a = dvdt = dvdx.dxdt
a = vdvdx = -v.2α(2αx+β)2 = -2α.v.v2 = -2αv3
∴ Retardation = 2αv3