speed through practice. So use this method on all your homework problems, and when you feel
comfortable with it, you might want to use it on quizzes and tests. The other benefit to the table method,
besides speed, is consistency; it forces you to set up every kinematics problem the same way, every time.
This is a time-tested strategy for success on the AP exam.
Motion Graphs
You may see some graphs that relate to kinematics on the AP test. They often look like those in Figure
11.1 . We call these graphs by the names of their axes: For example, the top graph in Figure 11.1 is a
“position–time graph” and the second one is a “velocity–time graph.”
Figure 11.1 Typical motion graphs. (As an excercise, you may want to describe the motion these
represent; answers are at the end of this section.)Here are some rules to live by:• The slope of a position–time graph at any point is the velocity of the object at that point in time.
• The slope of a velocity–time graph at any point is the acceleration of the object at that point in time.
• The area under a velocity–time graph between two times is the displacement of the object during that
time interval.
It’s sometimes confusing what is meant by the area “under” a graph. In the velocity–time graphs below,
the velocity takes on both positive and negative values. To find the object’s displacement, we first find the
area above the t -axis; this is positive displacement. Then we subtract the area below the t -axis, which
represents negative displacement. The correct area to measure is shown graphically in Figure 11.2a .
Whatever you do, don’t find the area as shown in Figure 11.2b ! When we say “area,” we measure that
area to the t -axis only.