1. Predict
Predict whether distance and displacement magnitude will be equal at the end of each of the three routes. Explain.
MEASURE MOTION, DISCOVER THE DIFFERENCE
Average Velocity and Average Speed
One motion, two different measures.
Speed relates to distance travelled; velocity relates to displacement.
Choose a path, watch the motion and measure the difference.
THINK BEFORE YOU START
If you complete a lap and return to your starting point, what is your average velocity?
Select circular motion and complete the experiment.2. Run a controlled experiment
Choose the one-way route with T = 12 s. Record distance, displacement and both averages halfway through and at the end, including units.
3. Compare and measure
At fixed T, test the return and circular routes. Distinguish instantaneous velocity at a turning point from average velocity since the trial began.
4. Examine the relationship
Choose the one-way route and halve T. With distance and displacement unchanged, calculate the ratios of both averages. At the end of a closed route, average velocity is zero in both runs; the ratio 0/0 is undefined.
5. Conclusions and limits
Explain why average velocity magnitude ≤ average speed using your observations. State when equality holds and note that repetitions are independent trials.
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01 / MOTION AREA
ReadyChoose your trajectory
0,00 / 12 s
Path travelled
StartDrag to explore timeEnd
Each repetition is an independent trial with the same initial conditions. Measurements and averages start from that trial’s beginning; repositioning is not part of the motion. The graph’s horizontal axis is session time.
What changes if the same trajectory is covered in less time?03 / CHANGE OVER TIME
Distance accumulates. Displacement magnitude can decrease.
Distance travelled s Displacement magnitude |Δr|
The graph builds up to the selected instant; the highlighted vertical line marks the current time.Ask. Test. Explain.
Ask a question
What happens to average velocity and average speed when you return to the starting point?
Test it
Complete one circular trip. Compare distance, displacement and the averages.
Interpret the result
Does zero average velocity mean there was no motion?
04 / GRASP THE CONCEPT
Vectors and scalars: the difference
Average velocity is a vector. It points from the initial position to the final position. Average speed is a scalar and cannot be negative.
v̄ₛ denotes average speed; v̄ with an arrow denotes average velocity.
Equality holds when the motion stays on a straight path without reversing direction throughout the interval considered.
Model and assumptions
T is the duration of one independent trial; t is its local time, 0 ≤ t ≤ T. The object is a point particle with prescribed kinematics. No measurement error is added. Averages run from the start of the current trial to the selected instant.
Instantaneous velocities at the endpoints are the model’s one-sided limits from within the interval. The animation stopping does not mean that the object physically stops. The green arrow shows direction and relative magnitude, at a scale of 20 screen units per m/s.
Symbols and derivatives: how to read them
| Notation | Meaning and unit |
|---|---|
| Time; s denotes seconds. The light clock uses ns = 10⁻⁹ s. | |
| Displacement vector Δr (m), distance travelled s (m), elapsed time Δt (s). Δ means final minus initial; an arrow denotes a vector. | |
| The bar denotes an average. Arrowed v is average velocity; vₛ is average speed (m/s). | | denotes magnitude. | |
| x, y are position components (m); vₓ, vᵧ are velocity components (m/s). T is one independent trial’s duration (s); t in route equations is that trial’s local time. |
References and further reading
The books below offer further study of the relevant concepts. The simulation’s assumptions are stated separately above.
- David Halliday, Robert Resnick, Jearl Walker. Fundamentals of Physics. Edition 12 · Chapter(s) 2, 4. Wiley. View source ↗
- Hugh D. Young, Roger A. Freedman. University Physics with Modern Physics. Edition 15 · Chapter(s) 2, 3. Pearson. View source ↗
- Raymond A. Serway, John W. Jewett. Physics for Scientists and Engineers with Modern Physics. Edition 10 · Chapter(s) 2, 4. Cengage. View source ↗