how to find average velocity

June 27, 2026

To find average velocity , you look at how much your position changes (displacement) over how much time passes.

Average velocity=displacementtime interval\text{Average velocity}=\frac{\text{displacement}}{\text{time interval}}Average velocity=time intervaldisplacement

What “average velocity” really means

Average velocity tells you, on balance, how fast and in what direction you moved over a whole trip, not at any single instant.

It uses displacement , not total distance.
Displacement is “final position − initial position.”
Velocity includes direction, so it can be positive or negative depending on your chosen axis.

Example story:
You walk from home to a shop 300 m east, then back home. You’ve walked 600 m of distance, but your displacement at the end is 0, because you end where you started. So your average velocity for the whole trip is 0, even though you did a lot of walking.

Step‑by‑step: core formula

Use this when you know starting and ending positions and times.

Write down initial position x0x_0x0 and final position xfx_fxf.
Compute displacement: Δx=xf−x0\Delta x=x_f-x_0Δx=xf−x0.
Write down initial time t0t_0t0 and final time tft_ftf.
Compute time interval: Δt=tf−t0\Delta t=t_f-t_0Δt=tf−t0.
Apply the formula:

vavg=ΔxΔtv_{\text{avg}}=\frac{\Delta x}{\Delta t}vavg=ΔtΔx

Units will be like m/s, km/h, etc.

Mini‑example:
A runner goes from x1=60textmx_1=60\\text{m}x1=60textm to x2=40textmx_2=40\\text{m}x2=40textm in 4 s.

Δx=40−60=−20textm\Delta x=40-60=-20\\text{m}Δx=40−60=−20textm
Δt=4texts\Delta t=4\\text{s}Δt=4texts
vavg=−20/4=−5textm/sv_{\text{avg}}=-20/4=-5\\text{m/s}vavg=−20/4=−5textm/s (negative means “toward decreasing x”).

Special case: using initial and final velocities

If the acceleration is constant , there is a handy shortcut:

vavg=u+v2v_{\text{avg}}=\frac{u+v}{2}vavg=2u+v

uuu: initial velocity
vvv: final velocity

This is just the average of the two speeds, valid only when acceleration is uniform (like a car steadily speeding up).

Example:
A car speeds up from 10 m/s to 30 m/s with constant acceleration.

vavg=(10+30)/2=20textm/sv_{\text{avg}}=(10+30)/2=20\\text{m/s}vavg=(10+30)/2=20textm/s

Multiple segments: trip broken into pieces

If a trip has several parts with different velocities, the safest way is:

vavg=total displacementtotal timev_{\text{avg}}=\frac{\text{total displacement}}{\text{total time}}vavg=total timetotal displacement

For each segment, find displacement and time.
Add all displacements to get total displacement.
Add all times to get total time.
Divide total displacement by total time.

This is not usually the same as just adding all velocities and dividing by how many there are, unless each velocity lasted for the same amount of time.

From a graph or formula

If you have:

A position–time graph : pick two points, read off positions and times, then use Δx/Δt\Delta x/\Delta tΔx/Δt. Geometrically, the average velocity is the slope of the straight line between the two points.

A position function x(t)x(t)x(t): choose start time t1t_1t1 and end time t2t_2t2, compute x(t2)x(t_2)x(t2) and x(t1)x(t_1)x(t1), then:

vavg=x(t2)−x(t1)t2−t1v_{\text{avg}}=\frac{x(t_2)-x(t_1)}{t_2-t_1}vavg=t2−t1x(t2)−x(t1)

Quick HTML recap table

Here’s a compact HTML table to match your formatting rules:

html

<table>
  <tr>
    <th>Situation</th>
    <th>Formula for average velocity</th>
    <th>Key idea</th>
  </tr>
  <tr>
    <td>Basic definition</td>
    <td>v_avg = Δx / Δt</td>
    <td>Use displacement (final − initial position) over total time.</td>
  </tr>
  <tr>
    <td>Constant acceleration</td>
    <td>v_avg = (u + v) / 2</td>
    <td>Average of initial and final velocity when acceleration is uniform.</td>
  </tr>
  <tr>
    <td>Many segments</td>
    <td>v_avg = (Σ displacements) / (Σ times)</td>
    <td>Add all displacements and times; then divide.</td>
  </tr>
  <tr>
    <td>From position–time graph</td>
    <td>v_avg = (x2 − x1) / (t2 − t1)</td>
    <td>Slope of the straight line between two points.</td>
  </tr>
  <tr>
    <td>From position function x(t)</td>
    <td>v_avg = (x(t2) − x(t1)) / (t2 − t1)</td>
    <td>Evaluate function at two times and apply the basic formula.</td>
  </tr>
</table>

Tiny TL;DR

Use displacement, not total path length.
Core formula: vavg=Δx/Δtv_{\text{avg}}=\Delta x/\Delta tvavg=Δx/Δt.

With constant acceleration, you can also use vavg=(u+v)/2v_{\text{avg}}=(u+v)/2vavg=(u+v)/2.

Information gathered from public forums or data available on the internet and portrayed here.