Objectives (5 - 10 minutes)

1. Develop an understanding of the concept of instantaneous velocity, which is the velocity of an object at a specific point in its motion, usually represented by the tangent to the position-time curve at that point.
2. Apply the concept of average velocity to understand and calculate instantaneous velocity in uniform, accelerated, and decelerated motion.
3. Develop problem-solving skills related to instantaneous velocity, using the formulas and concepts learned.

Secondary Objectives

• Stimulate students' analytical and critical thinking by applying the theory learned in practical and real situations.
• Promote teamwork skills, encouraging discussion and sharing of ideas during the proposed activities.
• Foster students' curiosity and interest in Physics, showing the relevance of studying kinematics and its applications in everyday life.

During this initial stage, the teacher should clearly explain the lesson's objectives, presenting the concepts that will be studied and the skills that students should develop. For this, simple and everyday examples can be used to contextualize the theme and arouse students' interest.

Introduction (10 - 15 minutes)

1. Recalling Necessary Concepts: The teacher should start the lesson by recalling some important concepts that are the basis for understanding kinematics, such as the definition of motion, displacement, time, and average velocity. This review can be done interactively, with questions to students to assess the level of understanding and promote active participation.

2. Problem Situations: Next, the teacher should present two problem situations that will serve as a hook for the topic's Introduction. For example:

   • Situation 1: 'Imagine you are in a car that is accelerating. How can you know at what speed the car is going at a certain moment without looking at the speedometer?'
   • Situation 2: 'If you are watching a Formula 1 race on TV, how do the team engineers know the car's speed at a specific point on the track?'

3. Subject Contextualization: The teacher should then contextualize the importance of studying instantaneous velocity, explaining that this concept is fundamental for various areas of knowledge and practical applications. Some examples of applications may include: sports motion analysis, traffic engineering, weather forecasting, among others.

4. Topic Introduction: To introduce the topic in a way that captures students' attention, the teacher can use:

   • Curiosity 1: 'Did you know that an object's instantaneous velocity can be different from its average velocity? This is because instantaneous velocity refers to the speed at a specific point in motion, while average velocity is an average of all speeds over a certain time interval.'
   • Curiosity 2: 'Have you noticed that in some Formula 1 races, cars seem to be moving quickly, but they are actually just accelerating very fast? This happens because the instantaneous velocity is very high, even if the car's average velocity is lower.'
   • Practical Application: 'What if I told you that instantaneous velocity is even used in weather forecasting? Satellite images showing cloud movement are used to calculate the wind's instantaneous velocity at different altitudes and predict storm occurrences.'

By the end of the Introduction, students should have a clear understanding of the importance and context of studying instantaneous velocity, and be motivated and curious to learn more about the subject.

Development (20 - 25 minutes)

1. Theory - Definition and Calculation of Instantaneous Velocity (10 - 12 minutes): The teacher should start the theoretical part of the lesson by explaining the definition of instantaneous velocity. Then, introduce the formula for calculating instantaneous velocity in uniform motion, which is the derivative of the position-time equation with respect to time.

   • Step 1: Definition of Instantaneous Velocity: The teacher should explain that an object's instantaneous velocity is the speed it has at a specific point in its motion, meaning it is the speed it would have if it continued to move in the same way for a very short period of time.

   • Step 2: Calculating Instantaneous Velocity in Uniform Motion: The teacher should show the formula for calculating instantaneous velocity in uniform motion, which is V = ΔS/Δt, where V is the instantaneous velocity, ΔS is the displacement, and Δt is the time interval.

   • Step 3: Practical Examples: The teacher should exemplify the calculation of instantaneous velocity in uniform motion, using everyday situations that are easy for students to understand. For example, the movement of a clock's hand, the movement of a pointer on a car's speedometer, among others.

2. Theory - Calculating Instantaneous Velocity in Accelerated and Decelerated Motions (5 - 7 minutes): Next, the teacher should explain how to calculate instantaneous velocity in accelerated and decelerated motions, using the concept of acceleration.

   • Step 1: Definition of Acceleration: The teacher should explain that acceleration is the rate of change of an object's velocity over time.

   • Step 2: Calculating Instantaneous Velocity in Accelerated and Decelerated Motions: The teacher should show the formula for calculating instantaneous velocity in accelerated and decelerated motions, which is V = Vo + a.t, where V is the instantaneous velocity, Vo is the initial velocity, a is the acceleration, and t is the time interval.

   • Step 3: Practical Examples: The teacher should exemplify the calculation of instantaneous velocity in accelerated and decelerated motions, using everyday situations. For example, the movement of a car that is accelerating or braking, the movement of an elevator, among others.

3. Practice - Problem Solving (5 - 6 minutes): After the theoretical explanation, the teacher should propose some problems for students to solve, using the concepts and formulas learned. The problems should be varied, involving uniform, accelerated, and decelerated motions, and should be contextualized to make learning more meaningful and interesting for students.

   • Step 1: Presentation of Problems: The teacher should present the problems, explaining what is required and providing the necessary data for resolution.

   • Step 2: Problem Solving: Students should solve the problems individually or in groups, using the concepts and formulas learned. The teacher should move around the classroom, assisting students who have difficulties and encouraging discussion and sharing of ideas.

4. Review and Conclusion (5 - 7 minutes): The teacher should conclude the theoretical part of the lesson by reviewing the main points covered and addressing any student questions. Then, make the Conclusion, reinforcing the importance of studying instantaneous velocity and applying the concepts learned in practical situations.

   • Step 1: Review of Main Points: The teacher should review the main points covered in the lesson, recalling the definitions and formulas, and providing a brief recap of the examples and problems solved.

   • Step 2: Answering Questions: The teacher should open a space for students to ask questions and clarify points they may not have fully understood.

   • Step 3: Conclusion: The teacher should conclude the lesson, reinforcing the importance of studying instantaneous velocity, and encouraging students to continue practicing calculations and reflections at home.

By the end of this stage, students should have a clear understanding of the concept of instantaneous velocity and how to calculate it in different types of motions. Additionally, they should have developed their problem-solving skills and worked in teams during the practical activity.

Feedback (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): The teacher should promote a group discussion, where students have the opportunity to share their solutions and conclusions about the proposed problems. At this stage, the teacher can ask directed questions to stimulate everyone's participation and ensure that the concepts were understood correctly.

   • Step 1: Each group presents their solutions: The teacher can ask a representative from each group to present the solution to the problem they solved, explaining the steps they followed and the strategies they used.

   • Step 2: Discussion of Solutions: The teacher can ask questions to stimulate discussion, such as: 'Why did you choose this strategy to solve the problem?', 'How do you know the answer is correct?', 'Can you think of other ways to solve the problem?'.

   • Step 3: Correction of Solutions: The teacher should correct the solutions, pointing out errors and reinforcing correct answers. It is important for the teacher to explain errors constructively, showing students how to avoid these errors in the future.

2. Connection with Theory (2 - 3 minutes): After the discussion, the teacher should make the connection between the practice carried out and the theory studied. The teacher can ask students how they applied the concepts of instantaneous velocity and acceleration to solve the problems, and reinforce the importance of understanding the theory to be able to apply it in practice.

3. Individual Reflection (3 - 5 minutes): The teacher should propose that students reflect individually on what they have learned. The teacher can ask guiding questions for reflection, such as:

   • Step 1: What was the most important concept you learned today?
   • Step 2: What questions have not been answered yet?
   • Step 3: How can you apply what you learned today in other situations?

4. Sharing Reflections (2 - 3 minutes): The teacher should ask some students to share their reflections with the class. This is an opportunity for students to learn from each other and for the teacher to assess the class's level of understanding.

By the end of this stage, students should have consolidated their knowledge of the concept of instantaneous velocity, how to calculate it, and how to apply this concept in problem-solving. Additionally, they should have developed their communication and reflection skills, and had the opportunity to express their doubts and difficulties, which can facilitate the teacher's intervention to address these doubts.

Conclusion (5 - 10 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should start the Conclusion by summarizing the main contents covered in the lesson. The teacher can review the definitions of instantaneous velocity and acceleration, the formulas for calculating instantaneous velocity in uniform, accelerated, and decelerated motions, and the practical examples used to illustrate these concepts.

2. Theory-Practice Connection (2 - 3 minutes): Next, the teacher should explain how the lesson connected theory and practice. The teacher can highlight how theoretical concepts were applied in solving practical problems, and how practice helped consolidate the understanding of theoretical concepts.

3. Supplementary Materials (1 - 2 minutes): The teacher should suggest supplementary materials for students who wish to deepen their knowledge on the subject. These materials may include books, websites, videos, apps, among others, that offer detailed explanations and additional exercises on calculating instantaneous velocity.

4. Relevance of the Subject (1 - 2 minutes): Finally, the teacher should emphasize the importance of studying instantaneous velocity, explaining how this concept is applied in various areas of knowledge and in everyday situations. For example, the teacher can mention the importance of instantaneous velocity in sports motion analysis, traffic engineering, weather forecasting, among others.

5. Closure (1 minute): To conclude the lesson, the teacher should reinforce the importance of continuous study and practice for deepening knowledge, and encourage students to continue exploring the subject on their own.

By the end of this stage, students should have consolidated their knowledge of the concept of instantaneous velocity, how to calculate it, and how to apply this concept in problem-solving. Additionally, they should have understood the importance of studying instantaneous velocity and how this concept is applied in various areas of knowledge and in everyday situations.