When a perticle moves in straight line with constant acceleration, the following kinematic equations of motion can be used.
           (i)  v = u + at or  v = v₀ + at 
           (ii)  S = ut + (1/2) at²  or  x – x₀ = v₀ t + (1/2) at²
           (iii)  V² = u² + 2aS   or   V² = v₀² + 2a (x – x₀)
           (iv)   S_nth = u + (1/2) a(2n-1)
Where,
              u or v₀ is the initial velocity at t = 0.
              v is the final velocity at t = t.
              S is the total displacement in time interval t = (t₂ – t₁) = (t-0)
              a is the constant acceleration.
             S_nth is the displacement in nth sec of its motion i.e displacement in the time interval from                      t = (n – 1) to t = n.
For derivation of these equation CLICK BELOW
                  (i) pdf                       (ii) Video
NOTE: Motion under gravity is an example of motion in straight line with constant acceleration. We will consider motion under gravity separately.