Reading a graph
A graph shows a whole journey on one page. Its shape tells you what the motion was doing. The axes are the two lines with scales. Time is on the bottom one.
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- Draw the axes: time along the bottom.
- Add a scale on each axis.
- Plot each reading as a point.
- Join the points. The slope is the acceleration.
The rule
On a position-time graph, the slope is the velocity. On a velocity-time graph, the slope is the acceleration. These shapes are for motion in one direction.
The slope is how steep a line is: rise divided by run. Rise is how far the line goes up. Run is how far it goes along. Steeper means a bigger change.
On a position-time graph, rise is a change in position. Run is the time taken. So the slope is velocity.
On a velocity-time graph, rise is a change in velocity. So the slope is acceleration.
| Graph | Shape | Meaning |
|---|---|---|
| Position-time | Flat line | At rest |
| Position-time | Straight slanted line | Constant velocity |
| Position-time | Curve that steepens | Velocity increasing |
| Velocity-time | Flat line | Constant velocity, acceleration 0 |
| Velocity-time | Straight rising line | Constant acceleration |
| Velocity-time | Straight falling line, above the axis | Slowing at a constant rate |
Read a slope from two points on the line. Each point is written as (time, reading).
| Graph | Two points | Slope |
|---|---|---|
| Position-time | (1 s, 20 m) and (3 s, 60 m) | (60 − 20) ÷ (3 − 1) = 20 m/s |
| Velocity-time | (5 s, 2 m/s) and (15 s, 8 m/s) | (8 − 2) ÷ (15 − 5) = 0.6 m/s² |
First row: rise = 60 − 20 = 40 m. Run = 3 − 1 = 2 s. Slope = 40 ÷ 2 = 20 m/s.
Second row: rise = 8 − 2 = 6 m/s. Run = 15 − 5 = 10 s. Slope = 6 ÷ 10 = 0.6 m/s².
Watch out!
A graph is not a route map. It shows position or velocity against time. It does not show the path.