How can I use a position-time table to find average velocity over an interval?
Quick answer
Choose the earlier and later entries for the interval. Subtract the earlier position from the later position, then divide by the elapsed time: average velocity = (later position − earlier position) ÷ (later time − earlier time). Keep the sign of the position change. For example, moving from 3 m at 2 s to −5 m at 6 s gives −8 m ÷ 4 s = −2 m/s. This is the average for the interval, not necessarily the velocity at every instant. [S1]
The question, the details, the next step.
I have a position-time table and need the average velocity between two rows. What should I do first?
Identify the two entries that mark the interval: the earlier time and position, then the later time and position. Use the same rows for both calculations. For a one-dimensional table, calculate average velocity as (later position − earlier position) ÷ (later time − earlier time). In symbols, that is (x₂ − x₁)/(t₂ − t₁). [S1]
The order matters: subtract earlier from later in both the position calculation and the time calculation. That gives signed displacement divided by elapsed time, rather than just a distance divided by time.
Could you show a worked example with units and a negative result?
Assume the table uses metres for position and seconds for time, and has these two entries:
- Earlier entry: t₁ = 2 s, x₁ = 3 m
- Later entry: t₂ = 6 s, x₂ = −5 m
First find the changes:
- Position change: x₂ − x₁ = −5 m − 3 m = −8 m
- Elapsed time: t₂ − t₁ = 6 s − 2 s = 4 s
Then divide: average velocity = (−8 m)/(4 s) = −2 m/s.
The negative sign belongs in the answer. It records the direction of the position change relative to the table’s coordinate direction; taking an absolute value would remove that information. [S1]
Does −2 m/s mean the object moved at that speed the whole time?
No. It means the net position change over the chosen interval, divided by the elapsed time, is −2 m/s. That average describes the interval as a whole; it does not tell you the velocity at every instant within it. [S1]
A position-time table with only the two selected entries is enough for this interval average, but it does not establish how motion varied between those entries. If you need the velocity at a particular moment, this calculation alone does not provide it. Keep the answer tied to the interval you selected.
What can I check if my answer seems wrong or the units do not look right?
Check the row order, the signs, and the units. In the example, the later position is −5 m, so subtracting the earlier 3 m gives −8 m—not +8 m. The time change is 4 s, and dividing metres by seconds gives m/s. If the two times are identical, the elapsed-time denominator is zero, so this calculation cannot produce an average velocity for that pair.
A reusable setup is:
- Earlier: t₁ = [time and unit], x₁ = [position and unit]
- Later: t₂ = [time and unit], x₂ = [position and unit]
- Position change: x₂ − x₁ = [value and position unit]
- Elapsed time: t₂ − t₁ = [value and time unit]
- Average velocity: (x₂ − x₁)/(t₂ − t₁) = [value and position unit/time unit]
Keep the signed result, and state which two entries define the interval.
A practical checklist
Select the earlier and later table entries that bound the interval.
Subtract earlier position from later position; retain a negative sign if the result is negative.
Subtract earlier time from later time to find elapsed time.
Divide position change by elapsed time and write position units per time unit.
Label the result as an interval average, not a claim about velocity at every instant.
A few more useful answers
Should I use distance traveled instead of change in position?
For average velocity, use signed change in position (displacement), not total distance traveled. Keep the subtraction in later-minus-earlier order. [S1]
What does a negative average velocity tell me?
It indicates that the net position change is negative relative to the coordinate direction used in the table. [S1]
Can two entries tell me the velocity at a specific moment?
They give the average velocity over the interval between them, not the velocity at every instant. The calculation alone does not establish the instantaneous velocity. [S1]
Sources
References used for this guide.
- [S1] OpenStax University Physics Volume 1: Position, Displacement, and Average Velocity openstax.org · Checked