Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 51289
Acceleration
In this lesson students will learn to:
1.
2.
3.
4.
5.
6.
Identify changes in motion that produce acceleration.
Describe examples of objects moving with constant acceleration.
Calculate the acceleration of an object, analytically, and graphically.
Interpret velocity-time graph, and explain the meaning of the slope.
Classify acceleration as positive, negative, and zero.
Describe instantaneous acceleration.
Subject(s): Mathematics, English Language Arts, Science
Grade Level(s): 9, 10, 11
Intended Audience: Educators
Suggested Technology: Graphing Calculators,
Computer for Presenter, Computers for Students,
Probes for Data Collection, Basic Calculators, LCD
Projector
Instructional Time: 3 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: acceleration, free fall, constant acceleration, velocity, graph, vector, speed
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Reinforcement activities or exercises for acceleration (Students version).docx
Reinforcement activities or exercises for acceleration (Teacher version).docx
5_Falling for Gravity.docx
7_Unit 1 Assessment.docx
Figure for teacher guidance exercise.docx
Unit 1 Self Assessment (Answer Key ).pdf
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
As a result of this lesson students should be able to:
1. Identify changes in motion that produce acceleration.
2. Explain why circular motion is continuous acceleration even when the speed does not change.
3. Calculate acceleration as the rate at which velocity changes.
4. Graph acceleration on a velocity-time graph.
5. Define instantaneous acceleration.
Prior Knowledge: What prior knowledge should students have for this lesson?
page 1 of 6 At the beginning of this section students should know:
Motion is described as a change of position in relation to a frame of reference.
The distinction between speed and velocity.
Simple vector operations as addition and subtraction.
How to identify positive and negative integers on a number line.
Graphing Skills: Student should be able to identify the slope and its meaning in a linear graph.
Basic Algebra skills: How to calculate or determine areas of rectangles and other type of operations.
Be aware of a common student misconception: If an object is accelerating then the object is speeding up. Explain to students that this is true in a common, everyday
usage. But in scientific terms, acceleration refers to any change in velocity. Velocity is a vector including both speed and direction, so acceleration can be speeding up,
slowing down, or even just changing direction.
Guiding Questions: What are the guiding questions for this lesson?
The Guiding Questions will include the following:
1. How are changes in velocity described?
2. How can you calculate acceleration?
3. How does a velocity-time graph indicate acceleration?
4. What is the meaning of the area under the graph in a velocity-time graph?
5. When is an object moving with constant acceleration?
6. What is instantaneous acceleration?
Teaching Phase: How will the teacher present the concept or skill to students?
The concept of acceleration will be presented using an inquiry format. The teacher will do an opening demonstration:
Let a ball roll down an inclined rail and ask students for observations. Record all observations. To proceed, they must mention something to the effect that the ball
speeds up as it rolls down.
To obtain a more detailed description, ask students which observations are measurable. Make sure they include the observation that the ball speeds up as it rolls
down the rail. (Do not let them state the ball accelerates since we haven't defined acceleration yet!)
Ask students how they could measure speed directly. Lead them to the conclusion that they cannot, but that they can measure position and time.
Students should mark the position of the object at equal time intervals.
Time should be plotted as the independent variable.
The teacher can demonstrate this concept with a variety of constant acceleration motion examples such as a cart rolling down a track, a bowling ball rolling down
an access ramp, or a disc and axle rolling down a ramp of two parallel pieces of conduit pipe.
Timing variations could include using photo-gates, water clocks, pendulums and metronomes in addition to stopwatches.
Make sure that the angle of inclination is less than 30 degrees.
Initial position and speed must be zero. (See sample graphs below.)
The teacher should discuss experimental procedure and the verbal interpretation of the parabolic x-t graph. Students should be able to describe that the displacement
during each time interval increases over the previous time interval. Since the object travels greater distances in each successive time interval, the velocity is
increasing. Define Acceleration as a change in speed or velocity (increasing or decreasing) at a time interval. The teacher should present at this time a perfect
example of acceleration due to a change in speed or velocity--free fall: the movement of an object toward Earth solely because of gravity.
Students should have also written an expression for the straight-line graph: x = kt2 + b, where b --> 0. The units of the constant of proportionality (slope) are m/s2,
but k is not the acceleration of the object. Emphasize the x vs t2 relationship and correct use of units, however stating that the slope has the units of acceleration
would be premature, because that quantity has yet to be defined. (This type of reasoning should be assigned for gifted students.)
Explain that acceleration isn't always the result of change in speed. Ask students to provide you with examples of motion where they're moving with constant speed or
velocity, however their direction of motion changes continuously (a carousel, a bicycle on a circular path, etc.). Although you may have a constant speed, your change
in direction means you're accelerating.
Extend the discussion until you arrive to the point where some objects move with a change in both speed and direction at the same time; example roller coaster. The
cars reach the top of the incline. Suddenly, they plummet toward the ground and then whip around a curve. You are thrown backward, forward, and sideways as your
velocity increases , decreases, and changes in direction. Your acceleration is constantly changing because of changes in the speed and direction of the cars of the
roller coaster.
Explain constant acceleration is a steady change in velocity. That is, the velocity of the object changes by the same amount each second. For example an airplane's
acceleration may be constant during a portion of the its takeoff.
Explain the meaning of the slope in a velocity vs. time graph is acceleration and from the slope equation.
;
or
Summarize:
When an object speeds up the final velocity is greater than the initial velocity, so acceleration is positive (a>0)
When an object slows down the final velocity is smaller than initial velocity, so acceleration is negative (a<0)
When an object moves with a constant velocity then the final velocity and initial velocity are equal, so the object does not accelerate a=0
page 2 of 6 Explain from the graph v=f(t) above, that the instantaneous acceleration is how fast a velocity is changing at a specific instant. Example; A skateboarder moving
along a half-pipe changes speed and direction. As a result, his acceleration changes. At each moment he is accelerating, but his instantaneous acceleration is always
changing.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
After the content is presented or at different stages during the presentation of the content (optional) this activities or exercises should be completed by the students
under teacher guidance:
1. Represent the motion that would result from the following configuration: (See Attachment: Figure for teacher guidance exercise)
a) qualitative graphical representation of x vs. t
b) qualitative graphical representation of v vs. t
c) qualitative graphical representation of a vs. t
d) general mathematical expression of the relationship between x and t
e) general mathematical expression of the relationship between v and t
f) general mathematical expression of the relationship between a and t
Calculating Acceleration:
2. A rubber ball rolls down an incline table, starting from rest. After 5 seconds, its velocity is 10 meter per second. What is the acceleration of the ball?
Problem Solving Skills:
Read and Understand
What information are you given?
time(t) = 5 seconds
starting velocity (
final velocity (
) = 0 m/s
) = 10 m/s
Plan and Solve
What unknown are you trying to calculate?
acceleration (a) - ?
What equation contains the given quantities and the unknown?
Replace each variable with its known value.
down the table
Look back and Check
Is your answer reasonable?
In free fall acceleration, objects accelerate at a rate of 9.8
; if the table is not very steep, a value of 2
seems reasonable.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
At this point of the lesson, students should be able to complete the exercises on the reinforcement hand out. (See attachment, Reinforcement activities and exercises
for acceleration)
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher should conclude the lesson by reinforcing the following ideas:
1. Any changes in velocity or changes in direction or changes on both can be described as acceleration.
2. When an object's changes in velocity are the same for every time interval, the object is moving with constant acceleration.
3. When an object speeds up: if the final velocity is greater then initial velocity, the acceleration is positive (a>0). When an object slows down: the final velocity is
smaller than the initial velocity, so acceleration is negative (a<0). When an object moves with constant velocity: the final velocity and initial velocity are equal, so
the object does not accelerate a=0
4. To calculate acceleration use the equation:
5. The meaning of the slope in a speed vs. time graph is the acceleration of the object. It could be positive, negative or zero.
6. In a displacement vs. time graph a curved line represents the acceleration. To calculate the instantaneous acceleration on that graph, find the smallest change in
velocity at a specific instant.
Summative Assessment
The teacher will determine if the students have reached the learning targets for this resource by taking traditional multiple-choice, true and false, or fill in the blank
assessments. One of these assessments is included in the Attachment section of this lesson. Unit 1 Self Assessment. Bioscopes; by Charles Carpenter. (used with
permission)
page 3 of 6 Also, Unit 1 Activity 3 Falling For Gravity, you will find an excellent lab to monitor student gains through graphical analysis and critical thinking. (Optional
Assessment for collecting, organizing and graphing data)
Formative Assessment
The teacher will gather information both formally and informally about student understanding throughout the lesson. At the beginning of the class the teacher will
review previous content (distance, position, displacement, speed, velocity, and graphical analysis) to check their ability to understand acceleration. By asking quick
questions about these topics informally we have an idea about what they need to know before moving on to other more difficult topics.
Engaging:
Demonstrate through rolling an object down an incline, or release it from a certain height. This will catch students attention immediately; during this encourage
them to observe, describe, and explain what they see. The teacher will be able to gauge their understanding.
Reading and Writing:
Encourage students to read about acceleration in their core textbook, using the web, reading another physics book or through other resources and complete a
concept map to organize what they know about acceleration. The teacher will circulate and interact with the students while they do their work, checking their
progress through the activity and providing help.
A sample student created concept map: Chart.docx
Feedback to Students
Students will get feedback about their performance or understanding during the lesson in different stages during and after the class time:
Encourage students to check their ideas with a classmate and the teacher during the observation; through describing and explaining the opening demo.
Students will be able to assess their own understanding through their use of resources. The text or online resources will provide guidance to prove and support
their ideas. The homework assignment will reinforce their learning.
The teacher will review their work and be able to see if students are on the right track and redirect them if necessary.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Inclusion Students - Visually Impaired:
Students who are visually impaired may grasp the concept of acceleration by describing the feeling of the actions instead of just the observations. Consider the
following scenario:
When traveling in a closed car with your eyes closed, it is hard to tell how far you have traveled or how fast you are going. But you can feel accelerations.
How do you know when you are speeding up or slowing down?
(When speeding up, it feels as if you are pressed against the back of the seat. When you are slowing down, it feels as if you are pulled forward against the
seat belt.)
How can you tell if you are changing direction?
(You can feel yourself pulled to one side, away from the direction the car is turning.)
Extensions:
A good extension of this lesson could be to ask students to make a project where they apply the idea of acceleration to the design of a roller coaster. Students
should research a particular roller coaster and create a drawing or diagram of its features. Have them describe the motion of the roller coaster in terms of its
velocity and acceleration. (Students may work in pairs for this project)
Another group of students can conduct research to find out the time period (in seconds) in which different kinds of cars can accelerate from 0 to 60 mph. For
example, the Ford Escape, an SUV with a 3.0-liter V-6 engine, can accelerate from 0 to 60 mph in 8.5 s. Students should include a variety of models in their
research, such as full-size cars, compact cars, trucks, SUVs, gas-electric hybrids, and sports cars. Ask them to create a bar graph to compare their data. (For ESOL
and inclusion students)
Suggested Technology: Graphing Calculators, Computer for Presenter, Computers for Students, Probes for Data Collection, Basic Calculators, LCD Projector
Special Materials Needed:
Depending on your access and familiarity to the equipment, choose either Low or High Tech:
Low Tech:
Bowling ball
chalk
accessibility ramp
disc and axle
parallel-pipe ramp
Stopwatch
water clock, metronome or pendulum
Ticker tape
masking tape
markers
Graphical Analysis
High Tech:
Dynamic cars and tracks
page 4 of 6 large steel ball
photogates (2)
Computer
ULI interface
ULI timer
Graphical Analysis
Further Recommendations:
Make sure to set up the incline ramp less than 30 degrees: angles larger than 30 degrees will accelerate the ball or car too fast and the results might not be
accurate.
Also early on in the lesson discuss the position proportionality to time square, so when the students obtain their graph, they should be able to understand it.
Address the misconception about objects speeding up are accelerating, acceleration is a vector, it has magnitude and direction, so any changes in speed or any
changes in direction or any changes on both, will produce an acceleration on the object.
It is very important to guide the students to understand the different scenarios where acceleration could be positive, negative, or zero, as well as graphing them in
an acceleration vs. time graph.
Additional Information/Instructions
By Author/Submitter
Be aware that:
Students have a misconception about acceleration: if an object is accelerating then the object is speeding up.
Students may have difficulty rearranging the equation to solve for other variables, especially for
. Write the procedure clearly on the board and describe each
step.
SOURCE AND ACCESS INFORMATION
Contributed by: Rafael Suarez
Name of Author/Source: Rafael Suarez
District/Organization of Contributor(s): Miami-Dade
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Distinguish between scalar and vector quantities and assess which should be used to describe an event.
Remarks/Examples:
SC.912.P.12.1:
Distinguish between vector quantities (e.g., displacement, velocity, acceleration, force, and linear momentum) and
scalar quantities (e.g., distance, speed, energy, mass, work).
MAFS.912.N-VM.1.3 (+) Solve problems involving velocity and other quantities that can be represented by
vectors.
Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of
reference) as functions of time.
Remarks/Examples:
SC.912.P.12.2:
Solve problems involving distance, velocity, speed, and acceleration. Create and interpret graphs of 1-dimensional
motion, such as position versus time, distance versus time, speed versus time, velocity versus time, and
acceleration versus time where acceleration is constant.
Florida Standards Connections: MAFS.912.N-VM.1.3 (+) Solve problems involving velocity and other quantities that
can be represented by vectors.
Recognize that time, length, and energy depend on the frame of reference.
SC.912.P.12.9:
LAFS.910.RST.2.4:
LAFS.910.SL.2.4:
MAFS.912.F-IF.2.6:
MAFS.912.N-Q.1.1:
Remarks/Examples:
The energy E and the momentum p depend on the frame of reference in which they are measured (e.g. Lorentz
contraction).
Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a
specific scientific or technical context relevant to grades 9–10 texts and topics.
Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the
line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and
task.
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified
interval. Estimate the rate of change from a graph. ★
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units
consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. ★
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