Area means distance covered
The area under a velocity-time graph is the displacement.
Velocity times time
A car moves at a steady 20 m s⁻¹ for 6 s. You multiply the velocity by the time. The product is a number of metres.
On a velocity-time graph, what do you think that product looks like?
What this lesson covers
The idea
The area enclosed between a velocity-time graph and the time axis over a time interval equals the displacement in that interval.
Velocity times time
A car moves at a steady 20 m s⁻¹ for 6 s. You multiply the velocity by the time. The product is a number of metres.
On a velocity-time graph, what do you think that product looks like?
- The area between the graph line and the time axis
- The slope of the line
- The height of the line
Shade the area
Shade the graph for each car and read the area.
The area is the displacement
For the steady car, the shaded rectangle had area 20 m s⁻¹ × 6 s = 120 m, the displacement in 6 s. For the speeding-up car, the shaded part between 10 s and 20 s was a rectangle plus a triangle, 50 m + 25 m = 75 m. In both cases the area was the displacement.
The area enclosed between a velocity-time graph and the time axis over a time interval equals the displacement in that interval.
Notes
Area between a velocity-time graph and the time axis = the displacement in that interval.
Check yourself
The area enclosed between a velocity-time graph and the time axis gives…
A car moves at a steady 20 m s⁻¹ for 6 s. What is the area under its velocity-time graph?
Answer: 120 m
20 m s⁻¹ × 6 s = 120 m, which is the displacement.
Between 10 s and 20 s the shaded area of a car's graph is a rectangle of 50 m and a triangle of 25 m. What is the displacement in this interval?
Answer: 75 m
50 m + 25 m = 75 m.
Which part of a velocity-time graph gives the displacement?
- the acceleration. The acceleration is given by the slope of the graph, not by the area.
- the velocity at the last instant. The velocity at an instant is read from the height of the graph.
- the displacement in that time interval — correct. Yes!
- The area between the graph and the time axis — correct. Yes!
- The slope of the graph. The slope of a velocity-time graph gives the acceleration.
- The height of the graph at the end. The height gives the velocity at that instant, not the displacement.