Distance-time graphs
If an object moves along a straight line, the distance travelled can be represented by a distance-time graph.
Example
Calculate the speed of the object represented by the green line in the graph, from 0 to 4 seconds (s).
change in distance = (8 - 0) = 8 m
change in time = (4 - 0) = 4 s
\(speed = \frac{distance}{time}\)
\(speed = 8 \div 4\)
\(speed = 2~m/s\)
Question
Calculate the speed of the object represented by the purple line in the graph.
change in distance = (10 - 0) = 10 m
change in time = (2 - 0) = 2 s
speed = 10 梅 2
speed = 5 m/s
Distance-time graphs for accelerating objects
If the speed of an object changes, it will be accelerating or decelerating. This can be shown as a curved line on a distance-time graph.
The table shows what each section of the graph represents:
| Section of graph | Gradient | Speed |
| A | increasing | increasing |
| B | constant | constant |
| C | decreasing | decreasing |
| D | zero | stationary (at rest) |
| Section of graph | A |
|---|---|
| Gradient | increasing |
| Speed | increasing |
| Section of graph | B |
|---|---|
| Gradient | constant |
| Speed | constant |
| Section of graph | C |
|---|---|
| Gradient | decreasing |
| Speed | decreasing |
| Section of graph | D |
|---|---|
| Gradient | zero |
| Speed | stationary (at rest) |
If an object is accelerating or decelerating, its speed can be calculated at any particular time by:
- drawing a tangent to the curve at that time
- measuring the gradient of the tangent
As the diagram shows, after drawing the tangent, work out the change in distance (A) and the change in time (B).
\(gradient = \frac{vertical~change}{horizontal~change}\)
Note that an object moving at a constant speed is changing direction continually. Since velocity has an associated direction, these objects are also continually changing velocity, and so are accelerating.