The relation between time t and distance x is t = αx² + βx, where α and β are constants. The retardation in terms of velocity v is given by ___________.

 Differentiating the equation with respect to time, 1 = α (2x) (dx/dt) + β(dx/dt) dx/dt = v 1 = α (2x) (v) + β(v)----------- (1) x = (1- β(v))/(2 α (v))----------- (2) Again differentiating (1) with respect to time 0 = α (2x) (dv/dt) + (2αv)(dx/dt) + β (dv/dt) dv/dt = A (retardation) 0 = α (2x) (A) + (2αv)(v) + β (A) Substituting x in terms of v as in (2) we get A = -2αv³