The relation between time ‘t’ and distance x for a moving particle is t=αx2+βx where α and β are constants, If v is the velocity at distance x, then the retardation of the particle is

given relation time is t=αx2+βx differentiate w.r.t. displacement x dtdx=2αx+βvelocity=v=dxdt=12αx+β---(1)∴v=2αx+β−1differentiate w.r.t. x dvdx=−12αx+β−2(2α)substitute equation (1)dvdx=−2α2αx+β2=−2αv2  we know,a=v.dvdx         since a=dvdt=dvdtdxdx=dxdtdvdx=vdvdx a=−2αv3 retardation of the paticle=2αv3