Objective: Learn how to find the velocity of an object by looking at the slope (gradient) of its displacement–time graph.
Think of the graph as a map of a road. The steeper the slope, the faster you’re going. That’s exactly what we’ll use to calculate velocity.
The gradient (or slope) of a line is the “rise over run” – the change in vertical distance divided by the change in horizontal distance. In a displacement–time graph, the vertical axis is displacement s (meters), and the horizontal axis is time t (seconds). The gradient therefore gives us s/t, which is velocity v.
Mathematically: v = \frac{ds}{dt}.
If the line is perfectly straight, the average velocity is also the instantaneous velocity at any point on that line.
A car moves along a straight road. Its displacement–time graph is a straight line that passes through the points (0 s, 0 m) and (10 s, 200 m).
So the car’s velocity is 20 m s⁻¹.
| Symbol | Meaning | Units |
|---|---|---|
| s | Displacement | m |
| t | Time | s |
| v | Velocity (average or instantaneous) | m s⁻¹ |
| a | Acceleration | m s⁻² |
Tip 1: Always check the units. If you get a slope in m s⁻¹, you’ve found velocity.
Tip 2: For a straight line, the gradient is the same everywhere. You can pick any two points, even the endpoints.
Tip 3: If the graph is curved, remember that the gradient at a point gives the instantaneous velocity. Use a small segment around that point.
Tip 4: When the question asks for “average velocity,” use the overall change in displacement divided by the total time.
Tip 5: Practice sketching graphs from equations like s = vt + ½at² to see how the slope changes with acceleration.