AcademyOne-Dimensional Motion
Academy
Average Velocity
Level 1 - Physics topic page in One-Dimensional Motion.
Principle
Average velocity measures displacement per time interval. It is a rate of net change, so it can hide reversals that occurred inside the interval.
Notation
\(\bar{v}_x\)
average velocity
\(\mathrm{m\,s^{-1}}\)
\(\Delta x\)
displacement
\(\mathrm{m}\)
\(\Delta t\)
elapsed time
\(\mathrm{s}\)
\(d\)
total distance traveled
\(\mathrm{m}\)
Method
Start with displacement
\[\Delta x = x_f - x_i\]
Divide by time
\[\bar{v}_x = \frac{\Delta x}{\Delta t}\]
Speed uses distance
\[\text{average speed} = \frac{d}{\Delta t}\]
Distance counts path length; displacement counts net change.
The secant line below connects the initial and final states. Its slope is the average velocity for the interval, even if the actual path between the two states bends.
Use distance, not displacement, only when the question asks for average speed.
Rules
These are the compact results from the method above.
Average velocity
\[\bar{v}_x = \frac{\Delta x}{\Delta t}\]
Average speed
\[\text{average speed} = \frac{d}{\Delta t}\]
Examples
Question
A particle moves from
\[x_i=4\,\text{m}\]
to \[x_f=-2\,\text{m}\]
in \[3\,\text{s}\]
Find \[\bar{v}_x\]
Answer
\[\Delta x=-2-4=-6\,\text{m}\]
\[\bar{v}_x=\frac{-6}{3}=-2\,\text{m s}^{-1}\]
Checks
- Velocity can be negative.
- Speed is not negative.
- Returning to start gives zero average velocity.
- Units must be length over time.