LEARNING CYCLE ASSIGNMENT
Physical Science: Motion in Our World
MW4 Investigate the relationship among speed, time, and acceleration for objects that undergo
uniformly accelerated motion
Suggested time: 4-6 hours
A). Objectives of Unit:
1). Collect data about everyday objects using a variety of methods describing the position,
direction of motion, and speed of motion.
2). Construct and analyze distance-time and speed-time graphs of objects that undergo uniform
acceleration.
3). Describe quantitatively the relationship among velocity, time, and acceleration.
B). This is a suitable topic because:
Motion occurs throughout our physical world, from the easily observable motion of people and
vehicles to less observable motion of atoms or orbiting planets. Motion constantly surrounds us
and studying motion allows students to use essential skills such as numeracy (Numeracy
involves helping students to develop a level of competence that allows them to use mathematical
concepts in science), and their communication skills (Communication focuses on improving
students' understanding of language use in science).
C). Curriculum fit/objectives:
Fit: MW4 Investigate the relationship among speed, time, and acceleration for objects that
undergo uniformly accelerated motion, is placed as the second last module out of the five
modules in the Physical Science unit. This unit normally fits near the end because the final
objectives from module 5, such as finding the slope of a graph and using motion equations, use
the learned knowledge from module 4.
Objectives:
1). Students need to have varied hands-on experiences with moving objects in order to develop
strong conceptual understandings of position, speed, and acceleration.
2). Students use different methods of representing the motion of everyday objects, and
understand what the advantages/disadvantages of each method are.
3). Students are able to explain in their own words that motion of any object can be described by
its position, direction of motion, and speed. Motion can be measured and represented on a graph.
All motion is relative to whatever reference point the observer chooses. Since everything in the
universe is moving, there is no fixed reference point in space from which to measure all
movement.
D). Assessment for success of the unit:
E). Amount of Time:
Activity 1: “Wiffle Ball Physics” (45 minutes)
Goals/Objectives:
-Students should predict the shape of distance-time graphs and speed-time graphs for objects that
undergo uniformly accelerated motion and then conduct an experiment to gather data that will
support or refute their predictions.
-Students should make decisions regarding what object(s) to use for the experiment, what
variables are to be tested, what variables are to be controlled, how to collect data, how much data
to collect, how to organize the data, and how many trials to conduct. Students should represent
their data using both speed-time and distance-time graphs
Materials/Safety:
Safety: throwing and hitting balls and advise students not to fool around and to use caution when
others are nearby.
Concepts/Pre-requisite Knowledge:
Description of Activity:
In groups of four, each student is assigned a role: hitter, pitcher, timer, or measurer. The timer
times how long the ball is in the air after it leaves the bat. The batter should not move after
hitting the ball so that an accurate starting position can be obtained for the distance measurement.
The measurer takes note of where the ball first lands (not where the ball rolls to) and measures
the horizontal distance from the batter to this point; he or she also measures the vertical distance,
approximately from the batter’s shoulder to the ground. After students have collected their
data, they solve for the initial velocity of the ball. Clearly, this activity is a simplification of a
very complicated problem. However, even though air friction and rotational motion are
significant in the movement of the Wiffle ball, the effects of friction and spin can
be neglected without compromising the integrity of the investigation as a learning experience.
Students’ calculations of velocity may not be accurate, but they are useful for starting a
discussion about projectile motion, drag forces, how drag would affect the velocity, and how
drag force changes with different balls.
Kinematics equation for both directions:
∆x=Voxt + ½ axt2
∆y= Voyt + ½ ayt2
In these equations, ∆x is the distance traveled horizontally, ∆y is the distance traveled vertically,
v0 is the initial velocity, a is the acceleration, and t is time. Solving for initial velocity (v0x and
v0y) in each direction, we get:
Vox=∆x/t
Voy= ∆y/t – ½ ayt
In these equations, ax is assumed to be 0 and ay is acceleration due to gravity (or -9.8 m/s2).
Students need to measure horizontal distance traveled (∆x), vertical distance traveled
(∆y; a student’s shoulder height is a good approximation), and time spent in the air (t). In most
cases, ∆x will be positive and ∆y will be negative. (Note: Students often miss that change in
height is negative.) Their measurements can be used to calculate the initial velocity of the ball in
each direction.
Students calculate the total velocity of the batted ball (v0) using the Pythagorean theorem: (v02 =
v0x 2 + v0y2), and the angle (θ) using trigonometric functions (e.g., tan q = v0y / v0x).
Background Information:
Usually students work with pencil and paper to read and solve projectile motion problems. This
activity allows students to create their own problems by applying their abstract knowledge of
projectile motion to something familiar like a wiffle ball. Students can also experiment with the
effect of different bats (flats versus skinny) and balls (holes versus no holes). Students work in
small groups to discuss the following problems: “What information is needed to calculate the
initial velocity of the ball as it is hit by the batter?”. Teachers should not provide students with a
procedure but allow them to determine what data to collect and how to use it. Before going
outside, students in each group must show a diagram of the problem and how they propose to
solve it using the projectile motion equations. Students must solve equations in both the
horizontal (bat) and vertical (ball) direction.
In this experiment, there is not one right answer, and students can be successful regardless of
how they hit the ball. Through this simple activity, students practice solving projectile motion
problems and have fun in the process. Students’ active role in the creation and solution of the
problem makes this a valuable learning experience.
Questions to stimulate and check for understanding:
1. Is the velocity calculation you made accurate? What else would you measure to get a better
value?
2. How would the problem change if someone caught the ball, or if it landed in the stands?
3. How does the angle at which you hit the ball affect the time it spends in the air and the
distance traveled?
4. How does the velocity at which you hit the ball affect the time it spends in the air and the
distance traveled?
5. You have not measured the following variables, but think about their relationship to the
velocity of the ball hit. How do you think the ball’s velocity is affected by:
-the velocity of the pitched ball?
-the speed of the bat?
-a strong wind blowing toward you?
-a strong wind blowing away from you?
-using a tennis ball instead of a Wiffle ball?
Expected Answers: To accelerate an object is to change its velocity, which is accomplished by
altering either its speed or direction (like in case of uniform circular motion) in relation to time.
Acceleration can have positive and negative values. Any time that the sign (+ or -) of the
acceleration is the same as the sign of the velocity, the object will speed up. If the signs are
opposite, the object will slow down. Acceleration is a vector quantity. When either velocity or
direction changes, there is acceleration (or deceleration). The graph of velocity (m/sec.) vs.
time (sec.) is a straight line for accelerating objects.
acceleration = velocity / time
To accelerate an object requires the application of a force.
Source:
Lancor, R.. (2009). Wiffle ball Physics. The Science Teacher, 76(6), 58-62. Retrieved
November 14, 2010, from ProQuest Education Journals. (Document ID: 1864404161). Website:
http://proquest.umi.com.libproxy.uregina.ca:2048/pqdweb?index=2&sid=1&srchmode=1&vinst
=PROD&fmt=6&startpage=1&clientid=12307&vname=PQD&RQT=309&did=1864404161&scaling=FULL&ts=128977373
3&vtype=PQD&rqt=309&TS=1289773982&clientId=12307
Activity 2: Rev Your Engines! Linking Physical Science and math with car labs:
Rubber Band Car Drag Race and Car lab Project
Goals/Objectives:
-Students will use motion sensors and graphing calculators to gather data on the distance and
time cars traveled and will generate time versus distance graphs for their car.
-Students can describe quantitatively the relationship among velocity, time, and acceleration
Materials/Safety:
Drag Race: Tape, calculator, GM-CALC cable, motion detector, car, graphical analysis software,
force sensor.
Rubber Band Car: wooden skewers, ruler, scissors, washers, cardboard, corrugated cardboard,
tape rubber bands, poster putty, pencils/pens/markers.
Concepts/ Pre-requisite Knowledge: laws of motion, forces, speed, velocity, acceleration,
energy, distance, slope, science as inquiry.
Description of Activity:
Students will construct rubber band cars, race them, and work through a number of automotive
activities. Students will have to use motion sensors and graphing calculators to gather data on the
distance and time cars traveled and to generate time versus distance graphs for their car.
Part 1: “Rubber Band Car Design”, no content is presented, and the guidelines are minimal.
Students design a car that will go the fastest and furthest in a drag race. They are given access to
all the materials and each team receives an instruction sheet that gives students ideas of how to
attach thin cardboard wheels to the skewer axle, and how to attach the rubber bands to the back
axle and to the cardboard body.
Part 2: “Rubber Band Car Drag Race”, the data collection begins when students place their car
directly in front of a motion detector attached to a graphing calculator. Then they start the
program on their calculators to analyze data, and release the cars to start the race. On the
calculator, the velocity graph and slope are displayed; students should sketch the graph on the
team data sheet and note whether the graph is a straight or curved line. Students can then modify
their cars to improve their performance by trying different wheel sizes, weights, rubber bands, or
other modifications indicated by the trials.
Part 3: Going the Distance Station, students run several 3-second trials with the motion sensor
attached to a graphing calculator to measure how far and how fast their car goes. The purpose of
this station is to discover averages, experimental error, effects on distance, and probability.
Background Information:
The Car Lab Project is an introduction to teaching about forces and motion, which requires
analyzing motion mathematically and graphically, as well as computing acceleration through the
use of technology, “probeware”. Building the rubber band car and running drag races also
teaches potential and kinetic energy. It introduces scientific inquiry which allows students to
investigate design variables such as the wheel size, rubber band lengths, etc…The advantage of
using probeware technology is that students can immediately see the graph and make decisions
on the spot based on the data displayed. In addition, students can modify their designs and
quickly observe the results using the calculator-based graphs.
Questions to stimulate and check for understanding:
Lab sheet for rubber band car.
Data Collection and Analysis
Hypothesis:
Data:
Name:_______________________________________
_
Date:________________________________________
Front wheel diameter (cm)
Rear wheel diameter (cm)
Rubber band length (cm)
Trial 1 Trial 2
Weight:___________________________ N
Number of wraps:
Sketch time versus distance graph
Velocity: ______________________ m/s2
Car Lab Project directions and data sheets: http://21ctl.fi.ncsu.edu/msms/autolabs.html
Questions: check for understanding
1. Why is the slope of the time versus distance graph also velocity?
2. If the time versus distance graph is a straight line, what do you know about your car’s
velocity? Its acceleration?
3. If the time versus distance graph is a curved line, what do you know about your car’s velocity?
Its acceleration?
Expected answers:
If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is
changing, then the slope is changing (i.e., a curved line). If the velocity is positive, then the slope
is positive (i.e., moving upwards and to the right). The object has a positive or rightward velocity
(note the + slope). The object has a changing velocity (note the changing slope); it is
accelerating. The object is moving from slow to fast since the slope changes from small to big.
Source:
Blanchard, M., Sharp, J., & Grable, L.. (2009). Rev Your Engines! The Science Teacher, 76(2),
35-40. Retrieved November 14, 2010, from ProQuest Education Journals. (Document ID:
1647384091). Website <
http://proquest.umi.com.libproxy.uregina.ca:2048/pqdweb?index=3&sid=1&srchmode=1&vinst
=PROD&fmt=6&startpage=1&clientid=12307&vname=PQD&RQT=309&did=1647384091&scaling=FULL&ts=128976001
8&vtype=PQD&rqt=309&TS=1289760110&clientId=12307>