Read motion from a slope.
Displacement is a vector from initial to final position; distance adds the lengths of the path travelled. Average velocity is displacement divided by elapsed time. Velocity is the gradient of a position–time graph, and acceleration is the gradient of a velocity–time graph.
The signed area under velocity versus time gives displacement. Areas below the axis contribute negatively. Add absolute areas to find distance. A curved position graph can represent acceleration even if every position value is positive.
Velocity and acceleration
Explore the relationship
Initial velocity +3 m s⁻¹; constant acceleration. The graph area gives signed displacement.
Tap or focus a plotted point to read its values.
View plotted data as a table
| Series | Time / s | Velocity / m s⁻¹ |
|---|---|---|
| Velocity / m s⁻¹ | 0 | 3 |
| Velocity / m s⁻¹ | 0.133333 | 3.13333 |
| Velocity / m s⁻¹ | 0.266667 | 3.26667 |
| Velocity / m s⁻¹ | 0.4 | 3.4 |
| Velocity / m s⁻¹ | 0.533333 | 3.53333 |
| Velocity / m s⁻¹ | 0.666667 | 3.66667 |
| Velocity / m s⁻¹ | 0.8 | 3.8 |
| Velocity / m s⁻¹ | 0.933333 | 3.93333 |
| Velocity / m s⁻¹ | 1.06667 | 4.06667 |
| Velocity / m s⁻¹ | 1.2 | 4.2 |
| Velocity / m s⁻¹ | 1.33333 | 4.33333 |
| Velocity / m s⁻¹ | 1.46667 | 4.46667 |
| Velocity / m s⁻¹ | 1.6 | 4.6 |
| Velocity / m s⁻¹ | 1.73333 | 4.73333 |
| Velocity / m s⁻¹ | 1.86667 | 4.86667 |
| Velocity / m s⁻¹ | 2 | 5 |
| Velocity / m s⁻¹ | 2.13333 | 5.13333 |
| Velocity / m s⁻¹ | 2.26667 | 5.26667 |
| Velocity / m s⁻¹ | 2.4 | 5.4 |
| Velocity / m s⁻¹ | 2.53333 | 5.53333 |
| Velocity / m s⁻¹ | 2.66667 | 5.66667 |
| Velocity / m s⁻¹ | 2.8 | 5.8 |
| Velocity / m s⁻¹ | 2.93333 | 5.93333 |
| Velocity / m s⁻¹ | 3.06667 | 6.06667 |
| Velocity / m s⁻¹ | 3.2 | 6.2 |
| Velocity / m s⁻¹ | 3.33333 | 6.33333 |
| Velocity / m s⁻¹ | 3.46667 | 6.46667 |
| Velocity / m s⁻¹ | 3.6 | 6.6 |
| Velocity / m s⁻¹ | 3.73333 | 6.73333 |
| Velocity / m s⁻¹ | 3.86667 | 6.86667 |
| Velocity / m s⁻¹ | 4 | 7 |
| Velocity / m s⁻¹ | 4.13333 | 7.13333 |
| Velocity / m s⁻¹ | 4.26667 | 7.26667 |
| Velocity / m s⁻¹ | 4.4 | 7.4 |
| Velocity / m s⁻¹ | 4.53333 | 7.53333 |
| Velocity / m s⁻¹ | 4.66667 | 7.66667 |
| Velocity / m s⁻¹ | 4.8 | 7.8 |
| Velocity / m s⁻¹ | 4.93333 | 7.93333 |
| Velocity / m s⁻¹ | 5.06667 | 8.06667 |
| Velocity / m s⁻¹ | 5.2 | 8.2 |
| Velocity / m s⁻¹ | 5.33333 | 8.33333 |
| Velocity / m s⁻¹ | 5.46667 | 8.46667 |
| Velocity / m s⁻¹ | 5.6 | 8.6 |
| Velocity / m s⁻¹ | 5.73333 | 8.73333 |
| Velocity / m s⁻¹ | 5.86667 | 8.86667 |
| Velocity / m s⁻¹ | 6 | 9 |
| Velocity / m s⁻¹ | 6.13333 | 9.13333 |
| Velocity / m s⁻¹ | 6.26667 | 9.26667 |
| Velocity / m s⁻¹ | 6.4 | 9.4 |
| Velocity / m s⁻¹ | 6.53333 | 9.53333 |
| Velocity / m s⁻¹ | 6.66667 | 9.66667 |
| Velocity / m s⁻¹ | 6.8 | 9.8 |
| Velocity / m s⁻¹ | 6.93333 | 9.93333 |
| Velocity / m s⁻¹ | 7.06667 | 10.0667 |
| Velocity / m s⁻¹ | 7.2 | 10.2 |
| Velocity / m s⁻¹ | 7.33333 | 10.3333 |
| Velocity / m s⁻¹ | 7.46667 | 10.4667 |
| Velocity / m s⁻¹ | 7.6 | 10.6 |
| Velocity / m s⁻¹ | 7.73333 | 10.7333 |
| Velocity / m s⁻¹ | 7.86667 | 10.8667 |
| Velocity / m s⁻¹ | 8 | 11 |
Explore: Adjust acceleration and compare the velocity slope with the moving marker.
A runner goes 30 m east, then 10 m west in 10 s.
- Distance = 40 m; displacement = 20 m east.
- Average speed = 4 ; average velocity = 2 east.
Assumed knowledge
Signed numbers and triangle areas.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Distinguish distance, displacement, speed and velocity.
- Use graph gradients and signed areas.