Topic: Graphical Representation of Motion (Displacement-Time & Velocity-Time Graphs)
Class: SS1
Specific Objectives:
By the end of this lesson, students should be able to:
- Plot displacement-time graphs.
- Plot velocity-time graphs.
- Interpret graphs to determine speed, velocity, and acceleration.
Instructional Materials:
- Graph paper
- Rulers
- Chalkboard/Whiteboard
- Calculator
- Objects for motion experiments (toy cars, balls)
Step 1: Displacement-Time Graphs
Displacement-time graphs show how an object’s position changes over time. The y-axis represents displacement, and the x-axis represents time.
- A straight line indicates uniform motion (constant velocity).
- A curved line indicates changing velocity (acceleration).
- The slope of the line gives the velocity.
Example: An object moves 10 m every second for 5 seconds. Plot the displacement-time graph.
- Displacement at each second: 0, 10, 20, 30, 40, 50 m
- The slope = rise/run = (50 - 0) ÷ (5 - 0) = 10 m/s (velocity)
Activity: Students measure a rolling toy car and record displacement at each second, then plot the graph.
Step 2: Velocity-Time Graphs
Velocity-time graphs show how velocity changes over time. The y-axis represents velocity, and the x-axis represents time.
- A horizontal line indicates constant velocity.
- A sloped line indicates acceleration.
- The slope of the line gives the acceleration:
Slope = Change in velocity ÷ Change in time
- The area under the velocity-time graph gives displacement:
Displacement = Area under velocity-time graph
Example: A car accelerates uniformly from 0 to 20 m/s in 5 seconds.
- Slope = (20 - 0) ÷ 5 = 4 m/s² (acceleration)
- Area under the graph = (1/2 × base × height) = 1/2 × 5 × 20 = 50 m (displacement)
Activity: Students plot a velocity-time graph for a toy car accelerating uniformly and calculate displacement from the graph.
Step 3: Interpreting Graphs
-
Displacement-time graph:
- Slope = velocity
- Horizontal line = stationary object
- Upward slope = moving object
-
Velocity-time graph:
- Slope = acceleration
- Area under graph = displacement
- Horizontal line = constant velocity
- Sloped line = accelerating or decelerating
Example: If a displacement-time graph has a slope of 6 m/s, the object moves at a constant velocity of 6 m/s. If the slope increases, the object is accelerating.
Activity: Students are given sample graphs and asked to:
- Calculate velocity from displacement-time graph slope.
- Calculate acceleration from velocity-time graph slope.
- Find displacement using area under velocity-time graph.
Step 4: Formulas Summary
Slope of displacement-time graph = velocity
Slope of velocity-time graph = acceleration
Area under velocity-time graph = displacement
Summary
- Displacement-time graphs show how position changes with time; slope = velocity.
- Velocity-time graphs show how velocity changes with time; slope = acceleration, area = displacement.
- Graphs provide a visual way to analyze motion.
Evaluation
- Sketch a displacement-time graph for an object moving at 5 m/s for 10 s.
- Determine acceleration from a velocity-time graph where v changes from 0 to 20 m/s in 4 s.
- Explain what a horizontal line in a displacement-time graph represents.
Class Work
- Draw a velocity-time graph for a car accelerating from 0 to 12 m/s in 6 s.
- Determine displacement from a velocity-time graph showing constant velocity of 5 m/s for 10 s.
- Identify velocity and acceleration from given sample graphs.
Home Work
- Interpret a displacement-time graph of a moving object.
- Draw a velocity-time graph for an object moving at constant velocity.
- Calculate displacement from a velocity-time graph with a sloped line.
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