Kinematics Equation for 1 - D Motion with constant acceleration

1.3 EQUATIONS FOR RECTILINEAR MOTION

 If a particle changes its velocity from u to v in time t, with uniform acceleration a and undergoes a displacement S in that time, then

            (a) v = u + at   

            (b) s = ut + 1/2 at²

            (c) v² = u²+ 2as   

            (d) s = 1/2 t (u + v)

            (e) s = vt - 1/2 at²

            (f) If S_n is the displacement in the nth second, then, s_n^th= u + 1/2 a(2n -1)

            The quantities u, v, a and S are in the same straight line, but they may be positive or negative depending upon the sign convention.

1.4       MOTION UNDER GRAVITY 

            For vertical motion under gravity, taking upward direction as positive,

             (a) v = u + gt   

            (b) h = ut + 1/2 gt²

            (c) v² = u²+ 2gh   

            where v and u are upward velocities and h is upward displacement.