Average velocity is total displacement divided by total time. It carries the direction of the displacement.
Average velocity Total displacement divided by total time.
Step 1: Something to Notice
Watch first. The explanation comes later.
A runner completes a lap of a 400 m track in 50 seconds. Her average speed is 8 m/s and her average velocity is zero.
How can both be true of the same run?
Step 2: Find Out
Isolate the slope of the position graph and compare it with the velocity reported.
Step 1 — Predict
A runner completes a full lap. What is her average velocity?
Choose what you think will happen. You cannot see the experiment until you do — guessing first is what makes it worth watching.
Step 3: So Here Is Why
Now the explanation, after you have seen it happen.
Average speed uses distance instead
Total path length over total time. For a closed path it is large while the average velocity is zero.
Instantaneous velocity is a single moment
The slope of the position-time graph at that instant. What a speedometer reads.
Instantaneous velocity The velocity at a single moment — the slope of the position graph there.
They agree only for constant velocity
A straight position graph has the same slope everywhere, so every instant equals the average.
And averaging the endpoints is not the definition
That works only for constant acceleration. Displacement over time always works.
Average and instantaneous are different numbers
Average velocity is total displacement over total time. Instantaneous velocity is the value at one moment. A journey averaging 50 km/h may never actually have been traveling at 50.
Average speed is not the average of the speeds
Half a journey at 30 and half at 60 does not average 45, because more time is spent at the slower speed. Average speed is always total distance over total time.
Step 4: A Common Mistake
Lots of people think
“Average velocity is the average of the starting and final velocities.”
Step 5: Why Average Speed Cameras Cannot Be Beaten by Braking
The same idea somewhere new.
A conventional speed camera measures instantaneous speed at a point, so slowing for it and accelerating away defeats it. Average speed cameras measure the time between two points and divide the known distance by it, which is an average and cannot be reduced by any pattern of speeding and slowing that covers the distance in that time. It is the distinction between the two quantities turned into enforcement.
Step 6: Think It Through
Practice makes it stick.
One Lap
Problem 1 of 2
A runner laps a 400 m track in 50 s. What is her average velocity?
The Average Speed Camera
Problem 2 of 2
Why can average speed cameras not be beaten by braking for them?
How Fast, and Which Way
1 of 5
What does average velocity divide?
2 of 5
What does a speedometer show?
3 of 5
When do average and instantaneous velocity agree?
4 of 5
What does the slope of a position-time graph give?
5 of 5
Is averaging the starting and final velocities always valid?
Step 7: Quick Check
Show what you know.
Question 1 of 1
A runner finishes exactly where she started. What is her average velocity?
Step 8: Explain It in Writing
Claim, evidence, then reasoning.
The question
A runner laps a 400 m track in 50 s. Explain why her average speed is 8 m/s and her average velocity is zero.
Fill in all three boxes. The reasoning box is the one that matters most.
What You Found Out
- Average velocity is displacement over time; average speed is distance over time.
- For a closed path the average velocity is zero however fast you went.
- Instantaneous velocity is the slope of the position graph at one moment.
- Average and instantaneous agree only when the velocity is constant.