2014-15 SHC Physics
CAPM
Name: _________________________________
Constant Acceleration Particle Model
Physical Quantity
Description/Notes
Symbol
Units
Equations Summary:
CAPM Model Summary – Appraisals
CAPM 1 Motion Maps: I draw and interpret motion maps to represent the motion of an object moving with a changing velocity.
CAPM 2 Drawing Graphs: I draw and relate position-time, velocity-time and acceleration-time graphs for an object moving with a
changing velocity.
CAPM 3 Describing:
I describe the motion of objects moving with positive or negative acceleration.
CAPM 4 Reading Graphs: I use position-time and velocity-time graphs to solve problems.
CAPM 5 Equations:
I can solve problems using kinematics equations.
Next Generation Science Standards - Labs
NG 1 Key Question:
NG 2 Investigation:
NG 3 Analysis:
NG 4 Model:
NG 5 Explaining:
Asking Questions and Defining Problems
Planning and Carrying Out Investigations
Analyzing and Interpreting Data
Developing and Using Models
Constructing Explanations, Designing Solutions, Engaging in Argument from Evidence
Review:
1. Given the following position vs. time graph, draw a motion map with one dot for each second.
0m
5m
+
Draw a quantitative velocity vs time graph for the motion.
V (m/s)
Describe the motion of the object in words.
On a position time graph, the y-intercept tells me:
On a positon time graph, the slope tells me:
On a position time graph I can tell if the object is moving in a positive or negative direction by:
On a velocity time graph, the y-intercept tells me:
On a velocity time graph, I can see how fast the object is moving by looking at:
On a velocity time graph, I can tell if the object is moving in a positive or negative direction by:
t (s)
Challenge 1: Is it accelerating?
On your blog:
 Key question (NG 1)
 Your set-up, including a photo (NG 2)
 Clear explanation of the data you collected (NG 3)
 Describe clearly your methodology for proving that the object is speeding up (NG 4)
 HOW exactly does your data prove that the object is speeding up (NG 5)
Discussion 1: Motion Maps
Activity 1: Motion Detectors
Hint: Push “Collect” and then let the cart go when the clicking starts.
DO NOT let the cart hit the Motion Detector!! To the RIGHT in the picture is the positive direction.
Predict FIRST! USE PENCIL!!!!
1. Increasing speed in the positive direction
a. Without using the motion detector, observe the motion of the cart as it starts from rest and rolls down the
incline.
b. Draw a motion map. Include velocity and acceleration vectors.
c. Is the velocity positive or negative?
e. Predict the graphs describing the motion.
d. Is the acceleration positive or negative?
f. Record the graphs as displayed by the motion detector.
g. The slope of the
position-time graph is
(constant / increasing / decreasing)
and
(positive / negative)
and represents
______________________.
h. The velocity-time graph line is
(above/below) the x-axis
representing motion in the
(positive/negative) direction.
The slope of the
velocity-time graph is
(constant / increasing / decreasing)
and (positive / negative)
representing
______________________.
2. Decreasing speed in the positive direction
a. Without using the motion detector, observe the motion of the cart slowing after a light, BRIEF initial push.
Answer the following questions for the cart while coasting.
b. Draw a motion map including both velocity and acceleration vectors.
c. Is the velocity positive or negative?
e. Predict the graphs describing the
motion.
d. Is the acceleration positive or negative?
f. Record the graphs as displayed by the motion detector.
g. The slope of the
position-time graph is
(constant / increasing / decreasing)
and
(positive / negative)
and represents
______________________.
h. The velocity-time graph line is
(above/below) the x-axis
representing motion in the
(positive/negative) direction.
The slope of the
velocity-time graph is
(constant / increasing / decreasing)
and (positive / negative)
representing
______________________.
3. Increasing speed in the negative direction
a. Observe the motion of the cart starting from rest and rolling down the incline without using the motion
detector.
b. Draw a motion map including both velocity and acceleration vectors.
c. Is the velocity positive or negative?
e. Predict the graphs describing the
motion.
d. Is the acceleration positive or negative?
f. Record the graphs as displayed
by the motion detector.
g. The slope of the
position-time graph is
(constant / increasing / decreasing)
and
(positive / negative)
and represents
h. The velocity-time graph
line is (above/below) the x______________________.
axis representing motion in
the (positive/negative)
direction.
The slope of the
velocity-time graph is
(constant / increasing /
decreasing) and (positive /
negative) representing
______________________.
4. Decreasing speed in the negative direction
a. Observe the motion of the cart slowing after a light, BRIEF initial push without using the motion
detector. Answer the following questions for the cart while coasting.
b. Draw a motion map including both velocity and acceleration vectors.
c. Is the velocity positive or negative?
e. Predict the graphs describing the
motion.
d. Is the acceleration positive or negative?
f. Record the graphs as displayed by the motion detector.
g. The slope of the
position-time graph is
(constant / increasing / decreasing)
and
(positive / negative)
and represents
h. The velocity-time graph line is
(above/below) the x-axis
representing
motion in the
______________________.
(positive/negative) direction.
The slope of the
velocity-time graph is
(constant / increasing / decreasing)
and (positive / negative)
representing
______________________.
5. Up and down the ramp
a. Observe the motion of the cart after an initial light, BRIEF push without using the motion detector.
Answer the following questions for the cart while coasting.
b. Draw a motion map including both velocity and acceleration vectors.
c. Is the velocity positive or negative?
d. Is the acceleration positive or negative?
Does the direction of the velocity change?
Does the direction of the acceleration change?
e. Predict the graphs describing the
motion.
f. Record the graphs as displayed
by the motion detector.
g. The slope of the
position-time graph is…
h. The velocity-time graph line is….
The slope of the
velocity-time graph is
(constant / increasing / decreasing)
and
(positive / negative)
and represents
______________________.
Practice 1: Graphing Acceleration
1. Draw a motion map along the ramp for the motion of the ball as it rolls down the ramp from rest.
v o = 0 cm/s
x = 0 cm
x=25cm
x=50 cm
Draw graphs corresponding to the motion of the
ball in problem 1.
Draw graphs corresponding to the motion of the
ball in problem 2.
50 cm
2. Draw a motion map along the ramp for the motion of the ball as it rolls down the ramp from rest.
3. Draw a motion map along the ramp for the motion of the ball as it rolls up the ramp from a non-zero velocity.
Draw graphs corresponding to the motion of the
ball in problem 3.
Draw graphs corresponding to the motion of the
ball in problem 4.
4. Draw a motion map along the ramp for the motion of the ball as it rolls up the ramp from a non-zero velocity. Stop
drawing the graph when the ball reaches its highest point.
x = 0 cm
x=25cm
v o = 0 cm/s
x=50 cm
Graphing Summary
In a ___ graph I see ____
1
2
3
4
5
7
8
9
10
11
by looking at _____
Notes:
Practice 2: Stacks of Curves
Given the following position vs time graphs, sketch the corresponding velocity vs time and
acceleration vs time graphs. Next to each number, write if the forces are BALANCED or UNBALANCED.
For the following velocity vs time graphs, draw the corresponding position vs time and
acceleration vs time graphs.
Practice 3: Using Graphs
a. Where on the graph above is the object moving most slowly? How do you know?
b. Between which points is the object speeding up? How do you know?
c. Between which points is the object slowing down? How do you know?
d. Where on the graph above is the object changing direction? How do you know?
Lab 1: Ticker Tapes
Creating a Position vs. Time graph (together):
Use ticker tape to create a real motion map. (Be sure to get a photo of set-up.) The frequency of the timer is
40 Hz or 60 Hz. This means 40 dots/sec or 60 dots/sec. Figure out how many dots represent 0.1 sec.
Start at the first recognizable dot, and label it zero. Count dots and mark 0.1 second intervals. Number each
time interval on the tape. If you are unsure in this step, ask me!! If you mess this part up the whole lab is a
waste.
NOW - On your blog:





A summary of how you used the ticker tape as a real motion map to obtain the position and time data
points. Include a photo of set-up AND of ticker tape.
A data table for total time elapsed (x) and position (y). Don’t forget units!!
A graph of position vs time. Use the trendline function to obtain equation of the curve (ASK ME!).
Write the verbal model and math model for this graph (do not worry about units at this point. Also if
any number is close to zero or very small, you can leave it out.)
Describe what this graph tells you about the motion of the cart and HOW DO YOU KNOW?
Creating a Velocity vs. Time graph (together):
Next, look at your ticker tape. Notice the space in between the intervals that you marked. What does this
space represent? (Check with me BEFORE continuing.)
Label your paper graph with velocity on the y axis and time on the x axis. Don’t forget units! Now cut your
tape apart into intervals. Lay them on the paper graph x-axis in order of interval # (skinny side across x-axis).
Glue or tape them down. Draw a trendline for this graph.
NOW - On your blog:





A photo of your labeled graph.
Write the verbal model for this graph.
What does the slope of this graph tell you? You do not have numbers on this graph, but pay attention
to the units to see what the slope is telling you.
Describe what this graph tells you about the motion of the cart and HOW DO YOU KNOW?
Does this graph “say” the same thing as the position vs. time graph? Explain.
Challenge 2: Developing the Equations
You are given the following graphs for a cart rolling
down an incline, derived for Ticker Tape data.
Position vs. Time
Position (cm/sec)
100
y = 29.552x2
80
Verbal Model:
60
40
Math Model:
20
0
-20 0
0.5
1
1.5
2
Y-intercept:
Time (sec)
Velocity vs. Time
Velocity (cm/sec)
120
y = 60.931x
100
Verbal Model:
80
Math Model:
60
40
Slope:
20
0
0
0.5
1
Time (sec)
1.5
2
Y-intercept:
1. What does the slope of the velocity graph tell you? Rewrite this math model using ONLY variables.
2. Look at the constant in the equation for the position graph. How does this number compare to the
slope of the velocity graph?
3. Rewrite the position graph math model using ONLY variables. Use units to check to see if your
model makes sense.
Practice 4: Using the Velocity graph
Given the velocity vs. time graph, determine:
1.
2.
3.
4.
5.
6.
Describe the motion of the object.
Draw a motion map.
The object’s initial velocity.
The object’s acceleration.
The object’s displacement from 0-5 sec.
How would you find the displacement with an equation?
Given the velocity vs. time graph, determine:
1.
2.
3.
4.
5.
6.
Describe the motion of the object.
Draw a motion map.
The object’s initial velocity.
The object’s acceleration.
The object’s displacement from 0-5 sec.
How would you find the displacement with an
equation?
Given the velocity vs. time graph, determine:
1.
2.
3.
4.
5.
6.
Describe the motion of the object.
Draw a motion map.
The object’s initial velocity.
The object’s acceleration.
The object’s displacement from 0-5 sec.
How would you find the displacement with an
equation?
Read this: http://www.physicsclassroom.com/class/1DKin/Lesson-4/Determining-the-Area-on-a-v-t-Graph
Challenge 3: Ranking Task
1. Rank the graphs from most negative velocity to most positive velocity.
Most negative 1_____2 _____ 3_____ 4 _____ Most positive
2. Rank the graphs from lowest speed to the highest speed.
Lowest speed 1_____2 _____ 3_____ 4 _____ Highest speed
3. Rank the graphs from highest acceleration to the lowest acceleration.
Highest acceleration 1_____2 _____ 3_____ 4 _____ Lowest acceleration
4. Rank the graphs from lowest displacement to the highest displacement
Lowest displacement 1_____2 _____ 3_____ 4 _____ Highest positive
Practice 5: Using Graphs to Solve Problems
a. Give a written description of the motion.
v
(m/s)
b. Sketch a motion map. Be sure to include both velocity and
acceleration vectors.
9
6
(3
(0
-3
-6
-9
0m
+
c. Determine the displacement from t = 0s to t = 4 s.
d. Determine the displacement from t = 4 s to t = 8 s.
e. Determine the average acceleration of the object’s motion.
f. Sketch a possible x-t graph for the motion of the object.
Explain why your graph is only one of many possible graphs.
g. Use a Kinematics EQUATION to solve for the acceleration.
2
4
6
t
(s)
a. Give a written description of the motion.
b. Sketch a motion map. Be sure to include both velocity and
acceleration vectors.
8
6
4
2
v
(m/s) 0
-2
-4
-6
-8
0m
+
c. Determine the displacement from t = 0 s to t = 4 s.
d. Determine the displacement from t = 4 s to t = 8 s.
e. Determine the displacement from t = 2 s to t = 6 s.
f. Determine the object’s acceleration at t = 4 s.
g. Sketch a possible x-t graph for the motion of the object.
Explain why your graph is only one of many possible graphs.
2
4
6
t
(s)
Challenge 4: Acceleration of the Toy Car
Practice 6: Using Kinematics Equations
velocity (m/s)
1. A poorly tuned car accelerates from rest to a speed of 28 m/s in 20 s.
a. Make a well-labeled diagram of the situation.
b. Make a well-labeled graphical representation of the situation.
c. List given quantities and quantities to find as you determine:
i. What is the average acceleration of the car?
ii. How far does it travel in this time?
time (s)
velocity (m/s)
2. A bus initially moving at 20 m/s slows by 4 m/s each second.
a. Make a well-labeled diagram of the situation.
b. Make a well-labeled graphical representation of the situation.
c. List given quantities and quantities to find as you determine:
i. How much time does it take the bus to stop?
ii. How far does it travel while braking?
time (s)
velocity (m/s)
3. A physics student skis down a slope, with a constant acceleration of 2.0 m/s2 for 15 seconds.
a. Make a well-labeled diagram of the situation.
b. Make a well-labeled graphical representation of the situation.
c. Determine the length of the slope.
time (s)
velocity (m/s)
4. A mountain goat starts a rock slide and the rocks crash down the slope 100 m in five seconds.
a. Make a well-labeled diagram of the situation.
b. Make a well-labeled graphical representation of the situation.
c. Determine the acceleration of the rocks.
time (s)
Practice 7: Using Velocity Graphs
a. Give a written description of the motion.
b. Sketch a motion map. Be sure to include both velocity and
acceleration vectors.
0m
+
c. Determine the displacement from t = 0 s to t = 3 s.
d. Determine the displacement from t = 4 s to t = 8 s.
e. Determine the displacement from t = 2 s to t = 5 s.
f. Determine the object’s acceleration at t = 6 s.
g. Determine the object’s acceleration at t = 8 s.
h. Sketch a possible x-t graph for the motion of the object.
Explain why your graph is only one of many possible graphs
Constant Acceleration of a Particle Model Summary
Purpose: In this unit, students develop a model to describe a particle moving with a constant
acceleration. Students should be able to describe a particle's constant acceleration motion with the model, as
well as predict future aspects of the particle's motion.
THE CAPM GRAPH MODELS:
Position vs. Time Graphs
1. What do Position vs. Time graphs show you about the movement of an object?
2. What does the shape of a position vs. time graph show you about the velocity of an object? How do
you know?
3. What does the y-intercept of a position vs. time graph tell you about the motion of an object?
4. How do you use a position vs. time graph to find the displacement of an object?
Velocity vs. Time Graphs
1. What do Velocity vs. Time graphs show you about the movement of an object?
2. What does a horizontal line on a velocity vs. time graph show you about the velocity of an object?
3. What does the y-intercept of a velocity vs. time graph tell you about the motion of an object?
4. What does the area “under the graph/line” on a velocity vs. time graph represent?
5. Can you determine an objects position while looking at a velocity vs. time graph?
Acceleration vs. Time Graphs
1. What do Acceleration vs. Time graphs show you about the movement of an object?
2. What does a horizontal line on an acceleration vs. time graph show you about the movement of an
object?
3. What does the y-intercept of an acceleration vs. time graph tell you about the motion of an object?
4. What does the area “under the graph/line” on an acceleration vs. time graph represent?
5. Can you determine an objects position while looking at an acceleration vs. time graph?
THE CAPM MATHEMATICAL MODELS
1) vf = v0 + at
1. What does vf stand for?
2. What does v0 stand for?
3. What does a stand for?
4. What does t stand for?
5. From which graph (see graph types above) did we derive this equation?
6. How did we derive this equation from the graph you mentioned in question 5?
2) xf = x0 + v0t + ½at2
1. What does xf stand for?
2. What does x0 stand for?
3. What does vf stand for?
4. What does v0 stand for?
5. What does a stand for?
6. What does t stand for?
7. From which graph (see graph types above) did we derive this equation?
8. How did we derive this equation from the graph you mentioned in question 7?
3) vf2 = v02 + 2a(xf – xo)
1. What does xf stand for?
2. What does x0 stand for?
3. What does vf stand for?
4. What does v0 stand for?
5. What does a stand for?
6. From which graph (see graph types above) did we derive this equation?
7. How did we derive this equation from the graph you mentioned in question 6?