The gradient is the acceleration
The gradient is calculated in exactly the way it was on the previous section's graphs. What changes is what it gives you.
On a velocity–time graph the x axis represents time, so the gap between two x coordinates is an interval of time.
The gap between the corresponding y coordinates is the change in velocity over that interval.
Change in velocity divided by time is acceleration.
gradient = change in velocity ÷ time = acceleration
Working it out
| t (s) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| v (m s⁻¹) | 0 | 3 | 6 | 9 | 12 | 15 | 18 |
change in velocity = 18 − 0 = 18 m s−1
time taken = 6 − 0 = 6 s
acceleration = 18 m s−1 ÷ 6 s = 3 m s−2
Two gradients, two meanings
| Graph | y axis | Gradient gives |
|---|---|---|
| Displacement–time | Displacement (m) | Velocity (m s−1) |
| Velocity–time | Velocity (m s−1) | Acceleration (m s−2) |
What about a flat line?
A horizontal line on a velocity–time graph has zero gradient, so the acceleration is zero and the velocity is not changing. That is an object moving at uniform velocity — not one at rest.