Formula  Definition and explanations 
s_{av} = \dfrac{d}{\Delta t}
 s_{av} is the average speed (scalar) d is the distance Δ t is the time elapsed

v_{av} = \dfrac{x_f  x_i}{t_f  t_i} =\dfrac{\Delta x}{\Delta t}
 v_{av} is the average velocity (vector) Δ x is the displacement(vector) Δ t is the time elapsed

a_{av} = \dfrac{v_f  v_i}{t_f  t_i} =\dfrac{\Delta v}{\Delta t}
 a_{av} is the average acceleartion (vector) Δ v is the change in velocity (vector) Δ t is the time elapsed

v_{av} = \dfrac{v_i + v_f}{2}
 v_{av} is the average velocity (vector) v_{i} is the initial velocity (vector) v_{f} is the final velocity (vector)

v_{f} = v_{i} + a \Delta t
 v_{f} is the final velocity (vector) v_{i} is the initial velocity (vector) a is the acceleration (vector)

\Delta x = v_i \Delta t + \dfrac{1}{2} a (\Delta t)^2
 Δ x is the displacement (vector) v_{i} is the initial velocity (vector) a is the acceleration (vector)

\Delta x = v_f \Delta t  \dfrac{1}{2} a (\Delta t)^2
 Δ x is the displacement (vector) v_{f} is the final velocity (vector) a is the acceleration (vector)

\Delta x = \dfrac{v_f+v_i}{2} \Delta t
 Δ x is the displacement (vector) v_{f} is the final velocity (vector) v_{i} is the initial velocity (vector)

v^2_f = v^2_i + 2 a \cdot \Delta x
 v_{f} is the final velocity (vector) v_{i} is the initial velocity (vector) Δ x is the displacement (vector) a is the acceleration (vector)
