Speed and Velocity, Calculations for SS 1

Class: SS 1
Term: First Term
Week: 6
Age: 15 years
Duration: 60 minutes
Subject: Physics
Curriculum Theme: Interaction of matter, space, and time
Focal competence: Determining speed and velocity from calculations and graph plotting
Key competencies/values: Creativity and Innovation; Research and Problem Solving; Problem Solving; Innovation
Skills:

• Determining the speed and velocity of moving bodies from calculation
• Plotting of distance-time graphs and determining speed and velocity from the graphs

Previous Lesson: First Term Physics Examination
Topic: Speed And Velocity
Subject Matter: Meaning of speed and velocity, Calculation of speed and velocity

Specific Objectives

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

Cognitive Domain

• Define speed and velocity.
• Distinguish between speed and velocity.
• State the SI units of speed and velocity.
• Describe how speed is different from velocity.
• Deduce speed and velocity from the gradient of motion graphs.

Psychomotor Domain

• Measure speed and velocity of a moving body using appropriate instruments.
• Calculate speed and velocity of a moving body using relevant formulas.
• Plot distance-time and displacement-time graphs.
• Generate data to plot distance-time graphs and make deductions from them.

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
• The HeadTeacher Scheme of work For The New Revised Senior Secondary Education Curriculum (SSEC)
• A suitable Senior Secondary Physics textbook

Instructional Materials

The teacher will teach this lesson with the aid of:

• Trolley/Toy car
• Stopwatch
• Protractor
• Meter rule
• Graph sheets

Rationale for the Lesson

Understanding speed and velocity is fundamental to describing motion in physics and everyday life. This lesson helps students differentiate between scalar and vector quantities, apply mathematical formulas to real-world scenarios, and interpret graphical representations of motion, which are essential skills for further studies in science and engineering.

Prerequisite/Previous Knowledge

Students should have a basic understanding of distance, displacement, time, scalar quantities, and vector quantities.

Lesson Content/Board Summary

Speed and Velocity

Meaning of Speed

Speed is defined as the rate at which an object covers distance. It is a scalar quantity, meaning it only has magnitude and no direction.

Formula:

(text{Speed} = frac{text{Distance travelled}}{text{Time taken}})

SI Unit: The SI unit of speed is metres per second (m/s).

Meaning of Velocity

Velocity is defined as the rate of change of displacement of an object. It is a vector quantity, meaning it has both magnitude and direction.

Formula:

(text{Velocity} = frac{text{Displacement}}{text{Time taken}})

SI Unit: The SI unit of velocity is also metres per second (m/s).

Distinction Between Speed and Velocity

The main difference between speed and velocity lies in their nature as scalar and vector quantities:

1. Speed: A scalar quantity that describes how fast an object is moving, without specifying its direction. It is always positive.
2. Velocity: A vector quantity that describes how fast an object is moving and in what direction. It can be positive, negative, or zero, depending on the direction of displacement.

For example, a car moving at 60 km/h has a speed of 60 km/h. If it is moving at 60 km/h towards the East, then its velocity is 60 km/h East.

Calculations for Speed and Velocity

Formula for Speed

(v = frac{d}{t})

Where:

1. (v) = speed
2. (d) = distance travelled
3. (t) = time taken

Example 1 (Speed)

Question: A car travels a distance of 180 metres in 30 seconds. Calculate its speed.

Solution:

Step 1: Write the formula.

(v = frac{d}{t})

Step 2: Substitute the values.

(v = frac{180 text{ m}}{30 text{ s}})

Step 3: Simplify and write the answer.

(v = 6 text{ m/s})

Answer: The speed of the car is (6 text{ m/s}).

Formula for Velocity

(v = frac{s}{t})

Where:

1. (v) = velocity
2. (s) = displacement
3. (t) = time taken

Example 2 (Velocity)

Question: A runner covers a displacement of 400 metres North in 50 seconds. What is the runner’s velocity?

Solution:

Step 1: Write the formula.

(v = frac{s}{t})

Step 2: Substitute the values.

(v = frac{400 text{ m North}}{50 text{ s}})

Step 3: Simplify and write the answer.

(v = 8 text{ m/s North})

Answer: The velocity of the runner is (8 text{ m/s North}).

Graphs of Motion

Distance-Time Graphs

A distance-time graph plots the total distance covered by an object against the time taken. For uniform speed, this graph is a straight line passing through the origin.

The gradient (slope) of a distance-time graph represents the speed of the object.

(text{Speed} = text{Gradient} = frac{text{Change in distance}}{text{Change in time}})

Displacement-Time Graphs

A displacement-time graph plots the displacement of an object from its starting point against the time taken. For uniform velocity, this graph is a straight line.

The gradient (slope) of a displacement-time graph represents the velocity of the object.

(text{Velocity} = text{Gradient} = frac{text{Change in displacement}}{text{Change in time}})

Teaching Methods/Instructional Techniques

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

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Questioning/Recall

Teacher’s Activity: The teacher asks students to recall the meaning of distance, displacement, and time. The teacher then introduces the topic “Speed and Velocity” as ways to describe how objects move.

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

Learning Point: Prior knowledge recall

Step 2: Meaning of Speed

Time: 10 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher defines speed as the rate of distance covered per unit time, explains its scalar nature, states its formula, and identifies its SI unit (m/s). The teacher uses a meter rule and stopwatch to demonstrate measuring distance and time for a toy car, then guides students to calculate its speed.

Pupils’ Activity: Pupils listen, ask questions, observe the demonstration, and participate in a simple speed calculation.

Learning Point: Definition of speed

Step 3: Meaning of Velocity

Time: 10 minutes

Teaching Skill: Explanation/Comparison

Teacher’s Activity: The teacher defines velocity as the rate of change of displacement per unit time, emphasizing its vector nature (magnitude and direction). The teacher states its formula and SI unit (m/s) and briefly highlights how it differs from speed.

Pupils’ Activity: Pupils listen, take notes, and ask clarifying questions about velocity and its direction.

Learning Point: Definition of velocity

Step 4: Distinction between Speed and Velocity

Time: 5 minutes

Teaching Skill: Comparison/Discussion

Teacher’s Activity: The teacher leads a discussion on the key differences between speed and velocity, focusing on scalar vs. vector quantities and the role of direction. The teacher uses examples to make the distinction clear.

Pupils’ Activity: Pupils contribute to the discussion, provide examples, and note the differences.

Learning Point: Speed-velocity distinction

Step 5: Calculation of Speed and Velocity

Time: 10 minutes

Teaching Skill: Problem Solving/Guided Practice

Teacher’s Activity: The teacher presents the formulas for speed and velocity and works through the examples provided in the Board Summary. The teacher then guides students to work in groups to solve additional exercises using the formulas, possibly using data from the trolley/toy car activity to determine speed and velocity from calculation.

Pupils’ Activity: Pupils copy the formulas and worked examples, then solve exercises in groups, applying the formulas.

Learning Point: Speed/velocity calculations

Step 6: Graphs of Motion

Time: 5 minutes

Teaching Skill: Explanation/Interpretation

Teacher’s Activity: The teacher explains how distance-time and displacement-time graphs are plotted and how speed and velocity can be deduced from their gradients. The teacher shows simple examples of such graphs on the board or chart.

Pupils’ Activity: Pupils observe the graphs, listen to the explanations, and understand how to interpret gradients.

Learning Point: Graph interpretation skills

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. Define speed and velocity.
2. State the SI units of speed and velocity.
3. What is the main difference between speed and velocity?
4. A car travels 200 m in 25 s. Calculate its speed.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Speed/velocity 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 speed, velocity, their distinction, calculations, and graph interpretation into their notebooks.

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

Learning Point: Physics notes copying

Step 9: Conclusion

Time: 5 minutes

Teaching Skill: Summarization

Teacher’s Activity: The teacher briefly recaps the definitions of speed and velocity, their differences, and the importance of direction in distinguishing them. The teacher encourages students to observe motion around them and try to apply these concepts.

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

Learning Point: Speed/velocity concepts

Continuous Assessment/Further Study

Type: Homework/Practice Exercise

Instruction: Answer the following questions in your Physics notebook.

1. A cyclist travels 1.5 km in 5 minutes. Calculate the speed of the cyclist in m/s.
2. A bird flies 500 m East in 20 seconds. What is its velocity?
3. Explain why a car moving around a circular track at a constant speed does not have a constant velocity.
4. Draw a simple distance-time graph for an object moving at a constant speed of 10 m/s for 5 seconds.

Lesson Keywords

• Speed – Rate of distance covered.
• Velocity – Rate of change of displacement.
• Scalar quantity – A quantity with magnitude only.
• Vector quantity – A quantity with both magnitude and direction.
• Distance-time graph – Graph showing distance versus time, whose gradient gives speed.
• Displacement-time graph – Graph showing displacement versus time, whose gradient gives velocity.

Differentiation

For struggling learners, the teacher will provide simpler numerical examples and focus more on the definitions and distinction between speed and velocity. Advanced learners will be challenged with more complex calculation problems involving unit conversions and interpreting non-uniform motion from graphs, possibly including practical data generation using the ticker timer concept.

Suggested Lesson Videos

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