We reviewed the development of the equations related to constant acceleration. Acceleration is defined as the rate of change of velocity. Velocity has what we call a magnitude and a direction. So it can be changed in two ways: 1) change the magnitude (a.k.a. speed in this case); and 2) change the direction. We focused our attention on one-dimensional situations, so that our accelerations were mainly of the first type. Initially we considered the special case of objects that started from rest.

The displacement, change in position, was given by the formula of v_avet, where v_ave is the average velocity for the period under consideration and t is the time (duration) of the period under consideration. If we started from rest then the average velocity is one half of the final velocity. And if the acceleration is constant (does not change with time), then the final velocity is given by at. Putting the pieces together leads to the formula s = at²/2.

We next moved on to consider two-dimensional motion and more particularly a special case of two-dimensional motion known as projectile motion. In two-dimensional motion, the position is determined/represented by a pair of numbers, known as the components of the position. There are different schemes for "breaking" the position into components. One important one is to use the the vertical component (directed down, i.e. toward the center of the earth) and the horizontal component (which is perpendicular to the vertical component). In projectile motion the only force acting on the object in flight is gravity. Thus the object's horizontal component is described by a constant velocity situation, and the object's vertical component is described by a constant acceleration scenario. Thus projectile motin is no more than putting these two pieces together.