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
\(speed = \frac{distance}{time}\)
\(speed = 8 \div 4\)
\(speed = 2~m/s\)
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
\(speed = \frac{distance}{time}\)
\(speed = 10 \div 2\)
\(speed = 5~m/s\)
Distance-time graphs for accelerating objects - Higher
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-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 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).
\(gradient = \frac{vertical~change (A)}{horizontal~change (B)}\)
It should also be noted that an object moving at a constant speed but changing direction continually is also accelerating. The speed of an object in a particular direction., a vector quantity, changes if either the magnitude or the direction changes. This is important when dealing with circular motion.