Topic 6 of 6
Plotting motion graphs
Use the readings to plot a graph, then use its gradients to describe the motion.
This example connects the displacement-time gradient with the velocity-time height and area. Rectangle area is width x height; triangle area is half of that.
A trolley moves forwards at a constant 2 m/s for 2 s, waits for 2 s, then moves forwards at a constant 3 m/s for another 2 s. Its recorded displacements are shown below. We model the changes between stages as abrupt.
| Time / s | Displacement / m |
|---|---|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 4 |
| 4 | 4 |
| 5 | 7 |
| 6 | 10 |
Plot the displacement-time graph
- Put time on the horizontal axis and displacement on the vertical axis. Label both quantities and units.
- Choose uniform scales that use the space: 0 to 6 s and 0 to 10 m cover these readings.
- Plot the pairs. Join each stage with a straight line because the motion is stated to be uniform within that stage. For a smoothly changing motion, use an appropriate smooth curve.
- Check the interpretation: rising from 0 to 2 s, flat from 2 to 4 s, then a steeper rise from 4 to 6 s.
Worked example
Sketch the velocity-time graph
Use the gradients you just found: draw horizontal segments at 2 m/s from 0 to 2 s, at 0 from 2 to 4 s, and at 3 m/s from 4 to 6 s. Mark the abrupt changes at the boundaries; a real trolley takes time to change its velocity.
The area is (2 x 2) + (0 x 2) + (3 x 2) = 10 m. This agrees with the final displacement on the first graph. Average speed is 10 / 6 = 1.67 m/s to 3 significant figures.
When interpreting experimental data: a few readings tell you average motion between those times. They do not prove exactly what happened between measurements. Here the description supplies the assumption of constant speed within each stage. Repeated readings and sensible scales help you spot an anomalous value before drawing a trend.
Try another set of readings
This optional task uses a different trolley, moving forwards at a constant speed within each stage. Sketch both motion graphs, describe the three stages and find the total distance. You can use paper; there is no need to submit an answer.
| Time / s | Displacement / m |
|---|---|
| 0 | 0 |
| 2 | 6 |
| 4 | 6 |
| 6 | 8 |
Show the worked answer
On the displacement-time graph, join (0, 0) to (2, 6), then to (4, 6), then to (6, 8) with straight segments. Label the time axis in seconds and the vertical axis in metres.
The gradients are (6 - 0) / 2 = 3 m/s, (6 - 6) / 2 = 0 m/s, and (8 - 6) / 2 = 1 m/s. The trolley moves quickly, stops for 2 s, then moves more slowly.
On the velocity-time graph, draw horizontal segments at 3, 0 and 1 m/s over the same intervals. Its area is (3 x 2) + (0 x 2) + (1 x 2) = 8 m.
During the stop, the first graph stays at 6 m while the second stays at zero. Both lines are horizontal, but their vertical axes describe different quantities.