The gradient is the velocity
The velocity can be found by working out the gradient of the straight line. Here is why that works.
How a gradient is calculated
Take any two points on the line. Divide the difference between their y coordinates by the difference between their x coordinates.
Why that is the velocity
The x axis represents time, so the gap between the two x coordinates is an interval of time.
The y axis represents displacement, so the gap between the two y coordinates is the displacement that happened during that interval.
Displacement divided by time is velocity.
gradient = displacement ÷ time = velocity
Working it out
Choose two points a good way apart on the line — A (1, 3) and B (5, 15). The two dashed lines show the "rise" and the "run" between them.
| t (s) | 1 | 5 |
|---|---|---|
| s (m) | 3 | 15 |
difference in y coordinates = 15 − 3 = 12 m
difference in x coordinates = 5 − 1 = 4 s
gradient = 12 ÷ 4 = 3
So the velocity of the motion shown by this graph is 3 m s−1.
Choosing the points
The gradient of a straight line is the same everywhere, so any two points give the same answer. Still, picking two that are far apart is better — a small reading error then affects the result less.