The distance x covered by a body moving in a straight line in time t is given by the relation 2x2+3x=t. If v is the velocity of the body at a certain instant of time, its acceleration will be

Differentiating 2x2+3x=t with respect to t we have 4xdxdt+3dxdt=1        .....(i)Now dxdt=v,Therefore, 4xv+3v=1 or 4x+3=1/v.Differentiating Eq (i) with respect to time t, we have 4dxdt2+4xd2xdt2+3d2xdt2=0 or       4v2+4xa+3a=0 or             a=-4v24x+3                (ii) Where a=d2xdt2is the acceleration, But 4x+3=1/v.Using this in Eq.(ii) we get a=-4v3.