Describing motion - AQA
The movement of objects can be described using motion graphs and numerical values. These are both used to help in the design of faster and more efficient vehicles.
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 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) |
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).
\[gradient = \frac{vertical~change (A)}{horizontal~change (B)}\]
It should also be noted that an object moving at a constant speed but changing direction continually is also accelerating. Velocity, a vector quantity, changes if either the magnitude or the direction changes. This is important when dealing with circular motion.