Average velocity connects where an object starts and ends to how long the change takes. In one-dimensional motion, it is a signed (directional) quantity that describes overall motion across an interval.

Core idea: average velocity over a time interval

Average velocity is defined using an interval with a clear start time and end time. Because velocity is a vector in one dimension, its sign depends on your chosen positive direction.

Displacement and time interval

Displacement depends only on the initial and final positions, not on what happens in between (including reversals of direction).

A motion timeline showing multiple legs of a trip with arrows indicating direction and labeled segment lengths. Even with reversals, the net displacement $\Delta x$ is determined only by the start and finish locations, while distance would add all segment lengths. This makes the sign convention (right/left as positive/negative) concrete. Source

The time interval is similarly based only on the start and end times.

In typical AP Physics 1 contexts, $\Delta t$ is positive because time moves forward; negative $\Delta t$ usually indicates you swapped “initial” and “final.”

Average velocity definition and equation

Average velocity is not “the velocity halfway through” and it is not found by averaging speeds at different moments unless motion is special (for example, symmetric constant-acceleration cases).

A position–time curve with two marked points (often labeled $P$ and $Q$), where $\Delta x$ and $\Delta t$ are drawn to show the interval used to compute average velocity. The straight line through the two points represents the secant, whose slope equals $v_\text{avg}=\Delta x/\Delta t$ for that interval. This visually distinguishes an interval-based average from a single-moment (instantaneous) value. Source

The unit $,\text{m/s},$ is equivalent to $,\text{m}\cdot\text{s}^{-1},$.

Sign conventions and interpretation in 1D

To interpret the sign of $v_\text{avg}$, first choose a coordinate axis (for example, “right is positive”).

• If $\Delta x > 0$, then $v_\text{avg} > 0$: net motion in the positive direction.

• If $\Delta x < 0$, then $v_\text{avg} < 0$: net motion in the negative direction.

• If $\Delta x = 0$, then $v_\text{avg} = 0$: the object ends where it started, even if it moved in between.

Magnitude matters too: $|v_\text{avg}|$ gives the rate of positional change per time, ignoring direction.

How to compute average velocity from typical information

You can find average velocity from any representation that provides initial and final position and the elapsed time.

A position–time graph where average velocity over a chosen interval corresponds to the slope of the straight line connecting the interval’s endpoints. Because the slope is $\Delta x/\Delta t$, it visually encodes both magnitude (steepness) and sign (upward vs. downward trend) of $v_\text{avg}$. Source

From two position-and-time data points

Use the endpoints of the interval only.

• Identify $(x_i, t_i)$ and $(x_f, t_f)$.

• Compute $\Delta x = x_f - x_i$.

• Compute $\Delta t = t_f - t_i$.

• Divide: $v_\text{avg} = \Delta x/\Delta t$.

Over multiple segments of motion

If motion is described in stages, average velocity over the entire interval still uses the overall displacement and total elapsed time.

• Add displacements to get $\Delta x_\text{total}$ (include signs).

• Add times to get $\Delta t_\text{total}$.

• Compute $v_{\text{avg, total}} = \Delta x_\text{total}/\Delta t_\text{total}$.

Do not average segment velocities directly unless the segments have equal durations; otherwise you will weight the intervals incorrectly.

Common pitfalls to avoid

• Using distance instead of displacement in the numerator (this changes the meaning).

• Dropping the sign of $\Delta x$ and losing direction information.

• Mixing units (for example, minutes with seconds) without converting.

• Using intermediate turning points when the question asks for average velocity over a stated start-to-end time interval.