In the case of constant acceleration, the velocity increases linearly with time according to the equation v = v_o + a t where v is the velocity at time t, v_o is the initial velocity measured at time t = 0, and a is the acceleration. A plot of velocity versus time for this case of constant acceleration will give a straight line graph as shown in Figure 3.4 on page 41 of the text. The graph is a straight line because the time appears in the equation raised to the first power. The acceleration is the slope of the graph of velocity versus time. The greater the acceleration, the steeper the graph will be.

In the case of constant acceleration, the distance from the starting point increases with time according to the equation d = v_o t + (1/2) a t² . The time appears in this equation raised to the second power, so the plot of displacement versus time for constant positive acceleration will give a graph that curves upward to the right when the displacement is plotted on the vertical axis and time is plotted on the horizontal axis. This is shown in Figure 3.8 on page 44 of the text.

For a projectile, the motion in the horizontal direction is independent of the motion in the vertical direction. This fact simplifies the calculation of position of a projectile, because the motion can be divided into two separate portions: the horizontal motion for which the acceleration is zero and the vertical motion for which the acceleration is the constant acceleration of gravity directed downward.