Velocity And Acceleration

Lesson Plan

Title: Velocity and Acceleration Problem to be studied: Are Local Speed Limits and Traffic Controls Reasonable?

Suggested Grade Level:

Intro: This lesson is the second part of a section on motion. It will cover 3-5 days depending on the weather and extent of student dialogue. Content Standard(s): Pa Dept of Education Academic Standards of Science and Technology Content Standards: 3.4.12.C Analyze the principles of translational motion, velocity and acceleration as as they relate to free fall and projectile motion Process Standard(s): • 3.2.12.C Apply the elements of scientific inquiry to solve multi-step problems. • Design an investigation with adequate control and limited variables to investigate a question. • Organize experimental information using analytic and descriptive techniques. • Evaluate the significance of experimental information in answering the question. • Project additional questions from a research study that could be studied. OBJECTIVES: The student will • Plot the displacement vs. time to represent velocity. • Develop a plan for improving the current system • Demonstrate an understanding of velocity and acceleration • Organize experimental information into a report including conclusions and recommendations

12 Materials: Toy car, ramp, police car, road strips, stop watches, data tables, journals, lap top computers (6), websites, Notebooks (journals) watches, data tables, journals, lap top computers (6), websites, Notebooks (journals)

Overview of Unit The idea of this unit is to spiral the knowledge of the students from a moving toy car, to a Police car in the school yard, to observation and experimentation, to a design and inquiry that lest them open up to the world of possibility. Student groups work in the classroom, parking lot and on the roadway (1-3 blocks) in front of the school to assess the speed of the cars, the impact of the speed limits and traffic controls on velocity and acceleration These arguments are developed through various lab activities (experiments and simulations) and from online research. Each group will present the results of their inquiry in a formal presentation. Procedures: Engage: Arranger chairs in an oval. Use remote controlled car to circle the class and start and stop in given locations. Discuss the factors involved in the travel. Use a KWL on speed and acceleration. (Be sure to capture distance/second, and change in speed.) Show the drag race video and discuss the motion of the vehicles. Sample questions: What was the speed and acceleration? What does 6.8 seconds mean? Is that good or bad? Review the data gathering stage of the process. Establish the 4 questions that will help them build their experimental findings. Explore Identify the deliverable form the data collection that should include: • Designing a speed trap to capture the average speed, the max speed, the acceleration in both directions. • A data table and three separate plots showing the essential parameter.

Lesson Plan

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A new approach to traffic control, including preliminary design and model.

. Establish teams with a balance of commuters including bus, walkers. Step one, have the Police car accelerate from a standing start with one member of each team in the car to monitor the speed. Use the rest of the team to monitor the speed and time traveled from outside. Have the car run several trials including a constant acceleration, some constant velocity, and changing acceleration. Have the teams journal their findings, report out conclusions and generate questions for the other groups to test their findings. Collect the journals for overnight assessment looking for, Data, insights, Q&A, the distance the care traveled. What was the acceleration of the car?

Explain: During a typical trip to school, your car will undergo a series of changes in its speed. If you were to inspect the speedometer readings at regular intervals, you would notice that it changes often. The speedometer of a car reveals information about the instantaneous speed of your car; that is, it shows your speed at a particular instant in time.

The instantaneous speed of an object is not to be confused with the average speed. Average speed is a measure of the distance traveled in a given period of time; it is sometimes referred to as the distance per time ratio. Suppose that during your trip to school, you traveled a distance of 5 miles and the trip lasted 0.2 hours (12 minutes). The average speed of your car could be determined as

On the average, your car was moving with a speed of 25 miles per hour. During your trip, there may have been times that you were stopped and other times that your speedometer was reading 50 miles per hour; yet on the average you were moving with a speed of 25 miles per hour Speed and velocity Imagine that on your way to class one morning, you leave home on time, and you walk at 3 m/s east towards campus. After exactly one minute you realize that you've left your physics assignment at home, so you turn around and run, at 6 m/s, back to get it. You're running twice as fast as you walked, so it takes half as long (30 seconds) to get home again. There are several ways to analyze those 90 seconds between the time you left home and the time you arrived back again. One number to calculate is your average speed, which is defined as the total distance covered, divided by the time. If you walked for 60 seconds at 3 m/s, you covered 180 m. You covered the same distance on the way back, so you went 360 m in 90 seconds. Average speed = distance / elapsed time = 360 / 90 = 4 m/s.

Lesson Plan

The average velocity, on the other hand, is given by: Average velocity = displacement / elapsed time. In this case, your average velocity for the round trip is zero, because you're back where you started so the displacement is zero We usually think about speed and velocity in terms of their instantaneous values, which tell us how fast, and, for velocity, in what direction an object is traveling at a particular instant. The instantaneous velocity is defined as the rate of change of position with time, for a very small time interval. In a particular time interval delta t, if the displacement is , the velocity during that time interval is:

The instantaneous speed is simply the magnitude of the instantaneous velocity. Acceleration An object accelerates whenever its velocity changes. Going back to the example we used above, let's say instead of instantly breaking into a run the moment you turned around, you steadily increased your velocity from 3m/s west to 6 m/s west in a 10 second period. If your velocity increased at a constant rate, you experienced a constant acceleration of 0.3 m/s per second (or, 0.3 m/s2). We can figure out the average velocity during this time. If the acceleration is constant, which it is in this case, then the average velocity is simply the average of the initial and final velocities. The average of 3 m/s west and 6 m/s west is 4.5 m/s west. This average velocity can then be used to calculate the distance you traveled during your acceleration period, which was 10 seconds long. The distance is simply the average velocity multiplied by the time interval, so 45 m. Similar to the way the average velocity is related to the displacement, the average acceleration is related to the change in velocity: the average acceleration is the change in velocity over the time interval (in this case a change in velocity of 3 m/s in a time interval of 10 seconds). The instantaneous acceleration is given by:

As with the instantaneous velocity, the time interval is very small (unless the acceleration is constant, and then the time interval can be as big as we feel like making it). On the way out, you traveled at a constant velocity, so your acceleration was zero. On the trip back your instantaneous acceleration was 0.3 m/s2 for the first 10 seconds, and then zero after that as you maintained your top speed. Just as you arrived back at your front door, your instantaneous acceleration would be negative, because your velocity drops from 6 m/s west to zero in a small time interval. If you took 2 seconds to come to a stop, your acceleration is -6 / 2 = -3 m/s2. EXPAND Using the information gathered, determine a more effective way to control the cars considering: the impact of changing speed and the environmental impact. Assessment Strategies: (Evaluation) Formative Evaluation: Observation of team interactions and report outs. Periodic review of notebook and journaling. Design review. Have the teams plot the velocity and acceleration from the selected trials Observations of activities. (Rubric)

Lesson Plan

Summative Evaluation: Experiment reports (See attached rubric) . Experimental findings review Team reports of new designs.

Related Web Sites: www.cpphysic.homestead.com; www.physicslessons.com

Inquiry Report: acceleration

Lesson Plan

CATEGORY

Excellent

Good

Satisfactory

Needs Improvement

Question/Purpose

The purpose of the lab or the question to be answered during the lab is clearly identified and stated.

The purpose of the lab or the question to be answered during the lab is identified, but is stated in a somewhat unclear manner.

The purpose of the lab or the question to be answered during the lab is partially identified, and is stated in a somewhat unclear manner.

The purpose of the lab or the question to be answered during the lab is erroneous or irrelevant.

Drawings/Diagrams Clear, accurate diagrams are included and make the experiment easier to understand. Diagrams are labeled neatly and accurately.

Diagrams are included and are labeled neatly and accurately.

Diagrams are included and are labeled.

Needed diagrams are missing OR are missing important labels.

Journal/Notebook

Clear, accurate, dated notes are taken regularly.

Dated, clear, Dated, notes are Notes rarely taken accurate notes are taken occasionally, or of little use. taken occasionally. but accuracy of notes might be questionable.

Experimental Design

Experimental design is a wellconstructed test of the stated hypothesis.

Experimental design is adequate to test the hypothesis, but leaves some unanswered questions.

Experimental design is relevant to the hypothesis, but is not a complete test.

Experimental design is not relevant to the hypothesis.

Conclusion

Conclusion includes whether the findings supported the hypothesis, possible sources of error, and what was learned from the experiment.

Conclusion includes whether the findings supported the hypothesis and what was learned from the experiment.

Conclusion includes what was learned from the experiment.

No conclusion was included in the report OR shows little effort and reflection.

Participation

Used time well in lab and focused attention on the experiment.

Used time pretty well. Stayed focused on the experiment most of the time.

Did the lab but did not appear very interested. Focus was lost on several occasions.

Participation was minimal OR student was hostile about participating.