Position, Distance and Displacement on the x-y Coordinate System for SS 1

Class: SS 1
Term: First Term
Week: 2
Age: 15 years
Duration: 60 minutes
Subject: Physics
Curriculum Theme: Interaction of matter, space, and time
Focal competence: Locating position and measuring distance and displacement of bodies
Key competencies/values: Creativity and Innovation; Leadership; Innovation
Skills:

• Measuring the distance of a body
• Measuring displacement of a body

Previous Lesson: Time Intervals, Need
Topic: Position, Distance And Displacement
Subject Matter: Meaning of position using the x-y coordinate system, Meaning of distance and displacement

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• Explain the concept of position using the x-y plane.
• Explain the concepts of distance and displacement.
• Differentiate among position, distance and displacement with examples.
• Distinguish between distance and displacement.

Affective Domain

• Appreciate the importance of precise measurement in physics.
• Demonstrate creativity and innovation in problem-solving tasks.
• Show leadership qualities during group discussions.

Psychomotor Domain

• Locate the position of an object on a graph using the Cartesian coordinate system.
• Measure the distance and displacement of a body.
• Calculate the distance and displacement of a body.

Social Domain

• Collaborate effectively with peers in group activities.
• Participate actively in classroom discussions.

Reference Materials

The following resources were used in planning this lesson:

• 2025 New Revised Senior Secondary Education Curriculum (SSEC)
• Relevant State Unified Scheme of Work
• New School Physics for Senior Secondary Schools
• The HeadTeacher Scheme of work For The New Revised Senior Secondary Education Curriculum (SSEC)

Instructional Materials

The teacher will teach this lesson with the aid of:

• Graph book
• Meter rule
• Protractor
• Toy cars
• Whiteboard/Blackboard
• Markers/Chalk

Rationale for the Lesson

Understanding position, distance, and displacement is fundamental to studying motion in physics. These concepts provide the basis for describing how objects move and are essential for further topics like speed, velocity, and acceleration. This lesson helps students develop analytical skills and apply mathematical tools to real-world physical scenarios.

Prerequisite/Previous Knowledge

Students should have a basic understanding of coordinate geometry (plotting points on a graph) and simple measurement using a ruler.

Lesson Content/Board Summary

Position, Distance and Displacement

Position on the x-y Coordinate System

Position refers to the location of an object relative to a reference point, often called the origin. In physics, we frequently use the Cartesian coordinate system (x-y plane) to specify position.

1. The x-y plane consists of two perpendicular number lines: the horizontal x-axis and the vertical y-axis.
2. The point where the x-axis and y-axis intersect is called the origin (0,0).
3. The position of any point (object) on this plane is described by an ordered pair of coordinates (x, y), where ‘x’ is the horizontal distance from the y-axis and ‘y’ is the vertical distance from the x-axis.
4. Positive x-values are to the right of the origin, negative x-values are to the left.
5. Positive y-values are above the origin, negative y-values are below.

Distance

Distance is the total length of the path covered by an object during its motion from one point to another, regardless of the direction of travel.

1. It is a scalar quantity, meaning it only has magnitude (a numerical value) and no direction.
2. The SI unit of distance is the metre (m).
3. Distance is always positive.
4. To measure distance, one traces the actual path taken by the object.

Displacement

Displacement is the shortest straight-line distance between an object’s initial position and its final position, along with the direction of that straight line.

1. It is a vector quantity, meaning it has both magnitude and direction.
2. The SI unit of displacement is the metre (m).
3. Displacement can be positive, negative, or zero.
4. If an object returns to its starting point, its displacement is zero, even if it has covered a significant distance.

Distinction Between Distance and Displacement

The key differences between distance and displacement are:

1. Nature: Distance is a scalar quantity, while displacement is a vector quantity.
2. Path dependence: Distance depends on the actual path taken by the object. Displacement only depends on the initial and final positions, not the path.
3. Value: Distance is always positive. Displacement can be positive, negative, or zero.
4. Magnitude: The magnitude of displacement can be less than or equal to the distance covered. It can never be greater than the distance.

Physical Quantities and Units

1. Position: Described by coordinates (x, y). The units for x and y are typically metres (m).
2. Distance: Scalar quantity. SI unit is the metre (m).
3. Displacement: Vector quantity. SI unit is the metre (m).

Calculation of Distance and Displacement

1. For motion along a straight line (1-D):

1. Distance: Sum of the magnitudes of all segments of the path.
2. Displacement: Final position minus initial position. (Delta x = x_f – x_i).

2. For motion in a plane (2-D) using coordinates:

If an object moves from an initial position (P_1(x_1, y_1)) to a final position (P_2(x_2, y_2)):

Formula for Displacement Magnitude

The magnitude of the displacement (|vec{d}|) is calculated using the distance formula:

(|vec{d}| = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2})

Where:

1. ((x_1, y_1)) = Initial coordinates
2. ((x_2, y_2)) = Final coordinates

The direction of displacement can be found using trigonometry (e.g., (tan theta = frac{y_2 – y_1}{x_2 – x_1})).

Example 1: Calculating Distance and Displacement in 1-D

Question: A boy walks 5 m East, then turns around and walks 2 m West. What is his total distance covered and his final displacement?

Solution:

Step 1: Identify the movements.

Movement 1: 5 m East

Movement 2: 2 m West

Step 2: Calculate total distance.

Distance = Sum of magnitudes of all paths

Distance = 5 m + 2 m = 7 m

Step 3: Calculate final displacement.

Let East be positive (+ve) and West be negative (-ve).

Displacement = (+5 m) + (-2 m) = 3 m

Answer: The total distance covered is 7 m. The final displacement is 3 m East.

Example 2: Calculating Distance and Displacement in 2-D

Question: An object moves from point A (2, 3) to point B (6, 6) on a coordinate plane. Calculate the magnitude of its displacement.

Solution:

Step 1: Identify initial and final coordinates.

((x_1, y_1) = (2, 3))

((x_2, y_2) = (6, 6))

Step 2: Write the formula for displacement magnitude.

(|vec{d}| = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2})

Step 3: Substitute the values.

(|vec{d}| = sqrt{(6 – 2)^2 + (6 – 3)^2})

(|vec{d}| = sqrt{(4)^2 + (3)^2})

(|vec{d}| = sqrt{16 + 9})

(|vec{d}| = sqrt{25})

Step 4: Simplify and write the answer.

(|vec{d}| = 5 text{ m})

Answer: The magnitude of the displacement is 5 m.

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Group Work, Problem Solving.

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Questioning/Recalling

Teacher’s Activity: The teacher greets the students and asks them to recall what they understand by “location” or “where something is”. The teacher then introduces the topic: Position, Distance and Displacement.

Pupils’ Activity: Pupils respond to questions and listen attentively to the introduction.

Learning Point: Recalling location concepts

Step 2: Explanation of Position on x-y Coordinate System

Time: 10 minutes

Teaching Skill: Explanation/Illustration

Teacher’s Activity: The teacher explains the concept of position using the x-y coordinate system, drawing and labelling the axes, origin, and quadrants on the board. The teacher defines coordinates (x, y) and how they specify a unique point.

Pupils’ Activity: Pupils listen, observe the board illustration, and ask questions for clarification.

Learning Point: Understanding x-y position

Step 3: Locating Position on a Graph

Time: 10 minutes

Teaching Skill: Demonstration/Guided Practice

Teacher’s Activity: The teacher guides students to locate the position of various points (e.g., P(3,2), Q(-1,4), R(0,-5)) on a graph sheet, demonstrating the process first. (Activity 2)

Pupils’ Activity: Pupils actively participate by plotting points on their graph sheets as guided by the teacher.

Learning Point: Plotting coordinates accurately

Step 4: Introduction to Distance and Displacement

Time: 10 minutes

Teaching Skill: Explanation/Discussion

Teacher’s Activity: The teacher introduces the concepts of distance and displacement, highlighting that distance is the total path length while displacement is the straight-line distance from start to end with direction. The teacher uses simple real-life examples to illustrate.

Pupils’ Activity: Pupils listen, contribute to the discussion with their own examples, and ask questions.

Learning Point: Defining distance and displacement

Step 5: Differentiating Distance and Displacement

Time: 10 minutes

Teaching Skill: Comparative Analysis/Group Work

Teacher’s Activity: The teacher guides students to work in groups to discuss the differences between distance and displacement, focusing on scalar/vector nature, path dependence, and possible values. The teacher monitors and provides feedback. (Activity 1 part)

Pupils’ Activity: Pupils discuss in groups, identify differences, and share their findings with the class.

Learning Point: Distinguishing scalar and vector

Step 6: Measuring and Calculating Distance and Displacement

Time: 10 minutes

Teaching Skill: Demonstration/Problem Solving

Teacher’s Activity: The teacher demonstrates how to measure distance using a meter rule by moving a toy car from point A to B along a curved path and then along a straight line for displacement. The teacher then works through the examples for calculating distance and displacement on the board. (Activity 1 part)

Pupils’ Activity: Pupils observe the demonstration, participate in measurements, and copy the worked examples into their notebooks.

Learning Point: Measuring and calculating motion

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Explain what is meant by the position of an object.
2. Locate the point (-2, 5) on a graph sheet.
3. State two differences between distance and displacement.
4. A boy walks 4m North and then 3m East. Calculate his total distance and the magnitude of his displacement.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Assessing lesson understanding

Step 8: Note-Taking

Time: 10 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on position, distance, and displacement, including definitions, distinctions, and formulas, into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording key concepts

Step 9: Conclusion

Time: 5 minutes

Teaching Skill: Summarisation

Teacher’s Activity: The teacher briefly recaps the main points of the lesson, re-emphasising the difference between scalar (distance) and vector (displacement) quantities and their importance in describing motion. The teacher encourages students to observe these concepts in their daily lives.

Pupils’ Activity: Pupils listen and ask any final questions.

Learning Point: Consolidating lesson concepts

Continuous Assessment/Further Study

Type: Homework

Instruction: Answer the following questions in your notebooks.

1. Define position, distance, and displacement.
2. Plot the points A(1,1), B(5,1), and C(5,4) on a graph sheet.
3. If an object moves from A to B then to C in question 2, what is the total distance covered?
4. For the movement in question 3, what is the magnitude of the displacement from A to C?
5. Give two examples of situations where distance and displacement would be different.

Lesson Keywords

• Position – The location of an object relative to a reference point.
• x-y Coordinate System – A system using two perpendicular axes (x and y) to define positions in a plane.
• Origin – The point (0,0) where the x and y axes intersect.
• Distance – The total length of the path travelled by an object; a scalar quantity.
• Displacement – The shortest straight-line distance from an initial to a final position, including direction; a vector quantity.
• Scalar Quantity – A physical quantity that has only magnitude.
• Vector Quantity – A physical quantity that has both magnitude and direction.

Differentiation

For struggling learners: Provide pre-drawn graph sheets with axes labelled. Offer simpler 1-D examples for distance and displacement calculations. Pair them with more capable students during group activities.

For advanced learners: Challenge them to find the direction of displacement using trigonometry in 2-D examples. Ask them to consider scenarios where distance and displacement are equal or where displacement is zero but distance is not.

Suggested Lesson Videos

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