Physics · Grades 9–12
Velocity–time graphs: slope and area
Separate acceleration from displacement when interpreting a graph.
Learn the idea
Slope
The slope of velocity against time gives acceleration, not displacement.
Signed area
Area between a velocity curve and the time axis gives displacement. Regions below the axis contribute negatively.
Speed and direction
Negative velocity identifies a direction. A negative acceleration may slow or speed an object depending on velocity.
Piecewise motion
Split a graph into rectangles and triangles when their areas can be found exactly.
Worked examples
Velocity rises uniformly from 2 to 10 m/s in 4 s. Find acceleration.
Slope is (10 − 2)/4 = 2 m/s².
2 m/s²
Velocity is a constant −3 m/s for 5 s. Find displacement.
Signed area is −3 × 5 = −15 m.
-15 m
Check your understanding
What is represented by slope on a velocity–time graph?
- Mass
- Position directly
- Acceleration
Velocity rises uniformly from 0 to 6 m/s in 4 s. Find displacement.
How can total distance differ from displacement on a velocity–time graph?
Answers and marking notes
Answers and marking notes
- Acceleration
Acceleration is velocity change per unit time.
- 12 m
The triangular area is 0.5 × 4 × 6 = 12 m.
- Distance adds the magnitudes of all areas; displacement adds signed areas.
Credit the treatment of below-axis regions.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.