Case I              when acceleration (a) of the particle is a function of time i.e.

                        A = f(t)                    dv/dt = f(t)            dv = f(t)dt

                        Integrating both sides within limits, equation have,

 Case II             When acceleration a of the particle is a function of distance i.e.

                        a = f(x)                   dv/dt = f(x)              (dv/dt)*(dx/dt) = f(x)

                               v(dv/dx) = f(x)          vdv = f(x)dx

                        Integrating we get,                            

Case III            When acceleration of the given particle is a function of velocity i.e.,

                        a = f(v)                    dv/dt = f(v)

 The displacement by the body of particle in n^th second is given by,

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