Models, Frame of Reference, Vectors and Scalars

1. Explain why models do not perfectly describe reality.

2. Define kinematics and state why it must always have a frame of reference.

3. Calculate average speed & solve speed problems.

4. State the difference between average and instantaneous as applied to kinematics.

5. State the difference between vectors and scalars.

6. State the difference between distance and displacement.
7. State the meaning of the sign on a vector. It only indicates direction. It does not indicate if an object is speeding up or slowing down. 3x5
8. Calculate average velocities.

Homefun: Read 2.1 to 2.3 Serway, Write a paragraph describing a scene from a sport assuming the frame of reference is on the ball

Metacognition Problem Solving Question: Can I establish upper and lower limits on the result of your calculation? Always attempt to estimate upper and lower limits on a variable in order to evaluate whether it has been correctly calculated.

In real life there are no answer books. Determining if a solution is right or wrong is up to you.

Relevance: Kinematics can be used to analyze motions in everything from athletic activities to the motion of vehicles .

Lesson 1

Key Concept: Physics is made up of models. Average speed and velocity are significantly different because one is a scalar and one is a vector.

Purpose: Introduce physics as a science of modeling by using several models. 

Pre-assessment: Use the internet to answer questions 15 - 17 on the Basic Physics Savvy Quiz

Interactive Discussion: Objectives 1. A model is a simplified version of reality used for predictions. A Barbie doll is a model. What things can be predicted from Barbie? In what ways is she simplified? 

Interactive Discussion: Objectives 2-3.How can a stationary wall also be moving at nearly 1000 miles per hour? What concept in physics accounted for the difference between Ptolemy's geocentric model of the universe and Galileo's model (two person groups using internet)? Both can accurately predict the location of planets in the night sky.

Interactive Discussion: Objectives 3 - 7, What is velocity? What is a vector? What is the difference between average speed and average velocity?

Resources/Materials: Barbi Doll, VCR, The Abyss video, computers for internet access.

Formative Assessment: Group and individual problem solving on white boards.

Acceleration

9. For constant velocity, draw the v vs t, and x vs t curves, given various starting velocities and displacements. 3x5
10. Define acceleration.
11. Calculate average acceleration.

Homefun: Read 2.4 to 2.5 Serway, Questions 1 - 11 p.44-45

Read: Insultingly Stupid Movie Physics

Chapter 7, Creative Kinematics: Explosive Entertainment, pp 99 - 115

Metacognition Problem Solving Question: Has everyone in the group made an independent calculation? All the members of a group need to make the calculations. When there is agreement the calculations are usually right.

Lesson 2

Key Concept: Even a high quality model has errors which creep in due to simplifying assumptions and experimental errors.

Purpose: Create kinematic model of an event.. 

Interactive Discussion: Objectives, What does the slope and intercepts mean on the graphs in obj. 9? Introduce lab write-up standards and the concepts of errors in the model and experimental errors. 

Interactive Discussion: Objectives 10, What is acceleration? In what types of situations would average accel differ from instantaneous accel? When would the two be equal? What does a negative acceleration mean? 

Closing:  Are models in physics accurate or are they merely adequate?

Movie Scene Analysis (3 person groups): The Abyss, Scene where Harrison falls over an underwater cliff.

1. How could we determine if he falls at constant speed? 
2. What is the difference between his instantaneous and average speeds?

Resources/Materials: VCR, The Abyss video, stop watches, computers for use with Excell Spread Sheets.

Formative Assessment: Group and individual problem solving on white boards.

Summative Assessment: Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion) 

The Constant Acceleration Kinematics Equations

12. For constant acceleration, draw the a vs t, v vs t, and x vs t curves and write equations for each. 3x5

12. State the meaning of the slope at a point for the v vs t, and x vs t curves.

slope of v vs. t curve = acceleration

slope of x vs. t curve = velocity

14. Solve constant acceleration problems in one dimension. using the kinematic equations ( 3x5  you must memorize these equations):

v_f = at + v_o

x = 1/2 at² + v_ot + x_o

Remember, the above 2 equations are only good when acceleration is CONSTANT !!!

15. Recognize that all objects fall at the same rate of acceleration when they are in a uniform gravity field.

Homefun: Read 2.6 to 2.7 Serway prob. 1, 3, 5, 7, 9 page 46

Metacognition Problem Solving Question: Have I drawn a picture or sketched a graph of the problem?  Pictures tend to engage additional parts of the brain not stimulated by equations.

Relevance: A constant acceleration analysis can be used for understanding why falls and car wrecks are so deadly .

Lesson 3

Key Concept: Many useful real world problems can be modeled as having constant acceleration

Purpose: Learn to solve constant acceleration problems

Answer Home Work Questions:

Interactive Discussion: Objectives 11, 12 The 2 constant acceleration equations.

In Class Problem Solving (2 person groups): Constant accel problems

1. Bob stops the redneckmobile
2. Toto in the well 
3. Bambi on the highway 
4. Robin Hood shoots a flaming arrow

Formative Assessment: Group and individual problem solving on white boards.

Summative Assessment: Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion) 

How much would  reaction time affect the accuracy of the time obtained using a stop watch.

Derivatives

16. State the general meaning of a derivative.

the derivative at a point on a curve

=

the slope at the point on the curve

17. Find the derivative of a polynomial.
18. Given x = f(t)  or v = f(t) find  v = f(t) or a = f(t).

Metacognition Problem Solving Principle: Do the number of unknowns match the number of equations? Most problems in physics are solved by simply writing enough equations so that they can be solved simultaneously.

Relevance: Derivatives are a basic tool of calculus. Physics gives derivatives a physical meaning that can be visualized, leading to a better understanding.

Lesson 4

Key Concept: The derivative is simply the slope at a point. Velocities and accelerations are both derivatives.

Purpose: Work problems using the derivative of polynomials

Answer Home Work Questions:

Interactive Discussion: Objectives 15 - 17 What is a derivative and how does it relate to physics.

In Class Problem Solving: Constant acceleration problems

1. Batman punches accelerator
2. Batman slams brakes 

Interactive Discussion: Objectives 18

Resources/Materials: color markers, white board.

Formative Assessment: Group and individual problem solving on white boards.

Integration

19. State the general meaning of integration. State the meaning of the area under the curve of the a vs t and v vs t curves. (Note area under the curve is defined as area between the curve and x-axis.)

    area under a vs t curve = velocity area under v vs t curve = displacement

20. Given a = f(t)  or v = f(t) find  v = f(t) or x = f(t).

21. By looking at the direction of the velocity and acceleration vectors, state whether an object is slowing down or speeding up.

22. Given mass calculate weight.

    (Weight) = (mass) g

23. Draw the the a vs. t,  v vs. t, and x vs. t curves for a dropped object when there is air resistance. Label the terminal velocity on the graph.

24. Solve graphical kinematics problems.

• Given a graph of acceleration vs. time solve for velocities and displacements.

• Given a graph of velocity vs. time solve for accelerations and displacements.

• Given a graph of displacement vs. time solve for velocities and accelerations.

Homefun: 11 p. 46, 47 p. 50

Metacognition Problem Solving Question: After solving an equation and performing dimensional analysis, do the units on the left side of the equation match with the units on the right side? Always list and pay attention to units. This will help prevent algebra errors.

Relevance: Integration is a basic tool of calculus. Physics gives integration a physical meaning that can be visualized, leading to a better understanding.

Lesson 5

Key Concept: The integral is simply the area under the curve. 

Purpose: Work problems using the integration of polynomials

Answer Home Work Questions:

Interactive Discussion: Objectives 19 -20 What is integration and how does it relate to physics?

Demo 1: Show carpenter's form

In Class Problem Solving: integration problems

1. Reverse Batman punches accelerator
2. Reverse Batman slams brakes 

Interactive Discussion: Objectives 21 -22. Why is mass not the same thing as weight?

Demo 2: Drop book with sheet of paper on top.

Resources/Materials: carpenter's form, color markers, white board.

Formative Assessment: Group and individual problem solving on white boards.

Review of Objectives 1- 25 (2-3 days)

Formative Assessments:

1. Work review problems at the board

2. Discuss study guide

3. Take practice test.

4. Work online quiz

Metacognition Problem Solving Question: Can I still work the problems done in class, several hours or days later? Some amount of repetition on the exact same problems is necessary to lock in learning. It is often better to thoroughly understand a single example of a problem type than to work example after example understanding none of them completely.

Relevance: Good test preparation is essential to performance in physics class.

Summative Assessment: Unit exam objectives 1-22

Summative Assessment: Formal Physics Investigation