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 s.
change in distance = (8 - 0) = 8 m
change in time = (4 - 0) = 4 s
\(speed = \frac{distance}{time}\)
\(speed = \frac{8}{4}\)
\(speed = 2 m/s\)
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
\(speed = \frac{distance}{time}\)
\(speed = \frac{10}{2}\)
\(speed = 5 m/s\)
Distance-time graphs for accelerating objects
If the speed of an object changes, it will be The rate of change in speed (or velocity) is measured in metres per second squared. Acceleration = change of velocity 梅 time taken. or Slowing down or negative acceleration, eg the car slowed down with a deceleration of 2 ms鈦宦.. This can be shown as a curved line on a distance鈥搕ime 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 A straight line that just touches a point on a curve. A tangent to a circle is perpendicular to the radius which meets the 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 usually changing direction continually, eg moving in a circle. Since velocity has an associated direction, these objects are also continually changing The speed of an object in a particular direction., and so are accelerating.
The Moon and other satellites orbit the Earth at a constant speed, but are accelerating towards the Earth.