Note the Physics:

• The constant acceleration equations, v = v₀ + a t and r = r₀ + v₀ t + (1/2) a t² are vector equations; each of the terms is a vector and they add in the geometric fashion of vectors.
• Vectors with different units cannot be added together; e.g., a must be multiplied by the scalar t (time) in order to get a vector that has units of velocity to add to v₀.
• For constant acceleration, the average velocity over a time range t is given by half the sum of the initial and final velocities: v_avg = (v₀ + v)/2 = v₀ + (1/2) a t.