Velocity, Acceleration, and Displacement
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 straight line 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 Δ means “change in.” So Δv = vf − v 0 , where v (^) f means “final velocity” and v 0 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.)
Constant-Acceleration Kinematics Equations
Putting all of these definitions together, we can come up with some important lists. First, we have our five
variables: