Lesson Plan

Title: Velocity and Acceleration

Problem to be studied: Are Local Speed Limits and Traffic Controls Reasonable?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 TechnologyContent Standards:3.4.12.C Analyze the principles of translational motion, velocity and acceleration asas they relate to free fall and projectile motion

Process Standard(s):• 3.2.12.CApply 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

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 theschool yard, to observation and experimentation, to a design and inquiry that lest them open up to the world ofpossibility.

Student groups work in the classroom, parking lot and on the roadway (1-3 blocks) in front of the school toassess the speed of the cars, the impact of the speed limits and traffic controls on velocity and acceleration Thesearguments 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 classand 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 orbad?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.

Suggested GradeLevel:

12

Materials: Toy car, ramp,police car, roadstrips, stopwatches, datatables, journals,lap top computers(6), websites,Notebooks(journals)watches, datatables, journals,lap top computers(6), websites,Notebooks(journals)

Lesson Plan

• 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 tomonitor the speed. Use the rest of the team to monitor the speed and time traveled from outside. Have thecar 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 totest 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 wereto inspect the speedometer readings at regular intervals, you would notice that it changes often. Thespeedometer of a car reveals information about the instantaneous speed of your car; that is, it shows your

speed at aparticularinstant intime.

The instantaneous speed of an object is not to be confused with the average speed. Average speed is a measure ofthe distance traveled in a given period of time; it is sometimes referred to as the distance per time ratio. Suppose thatduring your trip to school, you traveled a distance of 5 miles and the trip lasted 0.2 hours (12 minutes). The averagespeed 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 timesthat you were stopped and other times that your speedometer was reading 50 miles per hour; yet on the average youwere 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 towardscampus. After exactly one minute you realize that you've left your physics assignment at home, so you turn aroundand 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) toget home again.

There are several ways to analyze those 90 seconds between the time you left home and the time you arrived backagain. One number to calculate is your average speed, which is defined as the total distance covered, divided by thetime. If you walked for 60 seconds at 3 m/s, you covered 180 m. You covered the same distance on the way back, soyou 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 thedisplacement is zero

We usually think about speed and velocity in terms of their instantaneous values, which tell us how fast, and, forvelocity, in what direction an object is traveling at a particular instant. The instantaneous velocity is defined as therate of change of position with time, for a very small time interval. In a particular time interval delta t, if thedisplacement 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 ofinstantly breaking into a run the moment you turned around, you steadily increased your velocity from 3m/s west to6 m/s west in a 10 second period. If your velocity increased at a constant rate, you experienced a constantacceleration 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, thenthe average velocity is simply the average of the initial and final velocities. The average of 3 m/s west and 6 m/swest is 4.5 m/s west. This average velocity can then be used to calculate the distance you traveled during youracceleration period, which was 10 seconds long. The distance is simply the average velocity multiplied by the timeinterval, so 45 m.

Similar to the way the average velocity is related to the displacement, the average acceleration is related to thechange in velocity: the average acceleration is the change in velocity over the time interval (in this case a change invelocity 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 thetime 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 yourinstantaneous acceleration was 0.3 m/s2 for the first 10 seconds, and then zero after that as you maintained your topspeed. Just as you arrived back at your front door, your instantaneous acceleration would be negative, because yourvelocity drops from 6 m/s west to zero in a small time interval. If you took 2 seconds to come to a stop, youracceleration is -6 / 2 = -3 m/s2.

EXPANDUsing 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 trialsObservations of activities. (Rubric)

Lesson Plan

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

Related Web Sites:

www.cpphysic.homestead.com; www.physicslessons.com

Inquiry Report: acceleration

Lesson Plan

CATEGORY Excellent Good Satisfactory NeedsImprovement

Question/Purpose The purpose of thelab or the questionto be answeredduring the lab isclearly identifiedand stated.

The purpose of thelab or the questionto be answeredduring the lab isidentified, but isstated in asomewhat unclearmanner.

The purpose of thelab or the questionto be answeredduring the lab ispartially identified,and is stated in asomewhat unclearmanner.

The purpose of thelab or the questionto be answeredduring the lab iserroneous orirrelevant.

Drawings/Diagrams Clear, accuratediagrams areincluded and makethe experimenteasier tounderstand.Diagrams arelabeled neatly andaccurately.

Diagrams areincluded and arelabeled neatly andaccurately.

Diagrams areincluded and arelabeled.

Needed diagramsare missing ORare missingimportant labels.

Journal/Notebook Clear, accurate,dated notes aretaken regularly.

Dated, clear,accurate notes aretaken occasionally.

Dated, notes aretaken occasionally,but accuracy ofnotes might bequestionable.

Notes rarely takenor of little use.

ExperimentalDesign

Experimentaldesign is a well-constructed test ofthe statedhypothesis.

Experimentaldesign is adequateto test thehypothesis, butleaves someunansweredquestions.

Experimentaldesign is relevantto the hypothesis,but is not acomplete test.

Experimentaldesign is notrelevant to thehypothesis.

Conclusion Conclusionincludes whetherthe findingssupported thehypothesis,possible sources oferror, and whatwas learned fromthe experiment.

Conclusionincludes whetherthe findingssupported thehypothesis andwhat was learnedfrom theexperiment.

Conclusionincludes what waslearned from theexperiment.

No conclusion wasincluded in thereport OR showslittle effort andreflection.

Participation Used time well inlab and focusedattention on theexperiment.

Used time prettywell. Stayedfocused on theexperiment mostof the time.

Did the lab but didnot appear veryinterested. Focuswas lost onseveral occasions.

Participation wasminimal ORstudent washostile aboutparticipating.