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Velocity, Acceleration, and Displacement for AP Physics B & C

By — McGraw-Hill Professional
Updated on Feb 12, 2011

Practice problems for these concepts can be found at:

Kinematics Practice Problems for AP Physics B & C

We'll start with a few definitions.

In this definition, Δx means "displacement" and Δt means "time interval." Average speed is the total displacement you travel in a given time divided by the time it takes you to travel that distance. This is different from "instantaneous speed," which is your speed at any given moment. WARNING: The formula you learned in seventh grade, "speed = distance/time" is ONLY valid for an average speed, or when something is moving with constant speed. If an object speeds up or slows down, and you want to know its speed at some specific moment, don't use this equation!1

Questions on the AP exam tend to focus on velocity more than speed, because velocity says more about an object's motion. (Remember, velocity has both magnitude and direction.) Acceleration occurs when an object changes velocity.

The symbol Δmeans "change in." So Δv = vfv0, where vf means "final velocity" and v0 means "initial velocity" and is pronounced "v-naught." Similarly, Δt is the time interval during which this change in velocity occurred.

Just as velocity is the vector equivalent of speed, displacement is the vector equivalent of distance—it has both magnitude and direction.

So, let's say that you head out your front door and walk 20 m south. If we define north to be the positive direction, then your displacement was "–20 m." If we had defined south to be the positive direction, your displacement would have been "+20 m." Regardless of which direction was positive, the distance you traveled was just "20 m." (Or consider this: If you walk 20 m north, followed by 5 m back south, your displacement is 15 m, north. Your displacement is not 25 m.)

Fundamental Kinematics Equations

Putting all of these definitions together, we can come up with some important lists. First, we have our five variables:

Using just these five variables, we can write the three most important kinematics equations. An important note: The following equations are valid ONLY when acceleration is constant. We repeat: ONLY WHEN ACCELERATION IS CONSTANT. (Which is most of the time, in physics B.)2

We call these equations the "star equations." You don't need to call them the "star equations," but just be aware that we'll refer to the first equation as "*," the second as "**," and the third as "***" throughout this chapter.

These are the only equations you really need to memorize for kinematics problems.

Practice problems for these concepts can be found at:

Kinematics Practice Problems for AP Physics B & C

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