The relation between time t and distance x ist=αx2+βx where α and β are constants. The retardation is
2αv3
2βv3
2αβv3
2β2v3
dtdx=1V=2αx+βor V=12αx+β∴a=dvdt=dvdx⋅dxdt=vdvdx=−v⋅2a(2αx+β)2=−2αv3So, Retardation =2αv3