1. Why Do We Use Motion Graphs?
Graphs help us understand motion in a visual and simple way. Instead of reading long descriptions, we can quickly see how distance, speed, or velocity changes with time.
Motion graphs show how objects move using lines and curves, making patterns easy to notice.
1.1. Types of Motion Graphs
In kinematics, we mainly use two graphs:
- Distance–Time Graph
- Velocity–Time Graph
2. Distance–Time Graph
This graph shows how the distance travelled by an object changes with time. Distance is on the vertical (y-axis), and time is on the horizontal (x-axis).
2.1. Uniform Motion: Straight Line Graph
If an object covers equal distances in equal intervals of time, the graph is a straight line. The slope of the line represents speed.
2.1.1. Example
If a person walks 5 meters every second, the distance–time graph will be a straight upward line.
2.2. Non-uniform Motion: Curved Graph
If an object covers different distances in equal time intervals, the graph becomes curved. The curve shows changing speed.
2.3. Slope of the Distance–Time Graph
The slope of the graph gives the speed:
\( \text{Speed} = \dfrac{\text{Change in Distance}}{\text{Change in Time}} \)
3. Velocity–Time Graph
This graph shows how velocity changes with time. Velocity is on the vertical (y-axis) and time on the horizontal (x-axis).
3.1. Uniform (Constant) Velocity
If the velocity does not change, the graph is a horizontal straight line. The height of the line shows the value of velocity.
3.2. Uniform Acceleration: Slanting Straight Line
If velocity increases at a constant rate, the graph is a straight line slanting upward. The slope gives acceleration.
3.2.1. Slope = Acceleration
\( \text{Acceleration} = \dfrac{\text{Change in Velocity}}{\text{Change in Time}} \)
3.3. Uniform Deceleration: Slanting Downward Line
When velocity decreases at a steady rate, the graph slopes downward. The slope still gives acceleration, but it will be negative.
3.4. Area Under Velocity–Time Graph = Displacement
This is one of the most important facts about this graph. The area between the line and the time axis gives displacement:
\( \text{Displacement} = \text{Area under v–t graph} \)
4. Interpreting Motion from Graph Shapes
You can understand how an object is moving just by looking at the shape of the graph.
4.1. For Distance–Time Graphs
- Upward straight line → Uniform motion
- Curved upward line → Speed increasing
- Flat line (horizontal) → No movement (object at rest)
4.2. For Velocity–Time Graphs
- Horizontal line → Constant velocity
- Upward sloping line → Uniform acceleration
- Downward sloping line → Uniform deceleration
- Velocity becoming zero → Object stops
5. Examples of Motion Graphs in Real Life
Motion graphs are used in many real-life situations to analyze movement and performance.
5.1. Examples
- Speedometer data of a car being recorded over time.
- Graphs showing how an athlete’s speed changes during a race.
- Tracking the movement of a roller coaster on a ride.
- Recording the motion of planets or satellites.