Unit 2 Constant Velocity Physics Essential Standards Curriculum Assistance Document 2012
Essential Standards Phys 1.1 Analyze motion of objects
Unit
Constant Velocity
Time Allowed
8 days
Concepts
Frame of reference, position, vectors vs. scalars, motion maps, area under the curve
Vocabulary
Displacement, distance, position, velocity, speed
∆x = xf – xo ῡ = ∆x/∆t x = ῡt + xo ∆x = ῡt
Lab/Activities
Battery-powered vehicle lab: introduce motion maps, slope of line as velocity, change in position
Unit II worksheet 1 and Unit II Worksheet 2: graphical analysis practice; Motion Maps: representing
motion on a number line; Unit II Worksheet 4; Unit II Worksheet 5
Resources
Battery-powered vehicle lab
Apparatus
any slow-moving battery powered toy vehicle
Analysis
stop watches meter sticks
masking tape Graphical
Pre-lab discussion
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Let the vehicle move across table and ask for observations. List observations and then ask which items
are quantifiable. Lead them to observe that the tractor moves at constant speed; i.e., that it travels equal
distances in equal time intervals.
The dependent variable is position (x). Emphasize that we are dealing with position, not displacement or
distance traveled.
The independent variable is time (t). Emphasize time as a clock reading and not an interval of time.
(Why make time independent? Because when time is graphed on the horizontal axis the slope will be
equivalent to velocity.)
Lab performance notes
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•
Stopwatches and battery-powered vehicles are easier to use than "stomper" cars and photogates. (Honors
classes may be able to handle use of photogates at this stage.)
However you choose to have the students collect the data, they should be reminded to perform multiple
trials with at least 6 data pairs/trial. Averaging the values of position helps them develop a sense of the
precision they should carry through the analysis. Otherwise they are guilty of adhering to Lillenthal's
Laws:
1- If reproducibility is a problem, conduct only 1 test.
2- If a straight line plot is required, collect only two data points.
Post-lab discussion
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•
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Focus discussion on the position versus time relationship.
Use slope-intercept form to write equation of line (e.g. x  (0.85 ms )t  0.12m ).
Discuss the slope of the line as being a constant. Introduce the label units of slope (m/s).
Identify v (velocity) as the slope in the slope-intercept equation.
Discuss the vertical intercept and the "5% rule-of-thumb". In most cases, the intercept is negligible.
From specific equation, write general mathematical model x  v t . Discuss displacement (∆x) when
initial position is not zero.
UNIT II Worksheet 1
1. Consider the position vs. time graph below for cyclists A and B.
a. Do the cyclists start at the same point? How do you know? If not, which is ahead?
b. At t= 7s, which cyclist is ahead? How do you know?
c. Which cyclist is travelling faster at t = 3s? How do you know?
d. Are their velocities equal at any time? How do you know?
e. What is happening at the intersection of lines A and B?
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2. Consider the new position vs. time graph below for cyclists A and B.
a. How does the motion of the cyclist A in the new graph compare to that of A in the previous graph from
page one?
b. How does the motion of cyclist B in the new graph compare to that of B in the previous graph?
c. Which cyclist has the greater speed? How do you know?
d. Describe what is happening at the intersection of lines A and B.
e. Which cyclist traveled a greater distance during the first 5 seconds? How do you know?
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UNIT II: Worksheet 2
Sketch velocity vs time graphs corresponding to the following descriptions of the motion of an object.
1. The object is moving away from the origin at a
constant (steady) speed.
2. The object is standing still.
3. The object moves toward the origin at a steady speed
for 10s, then stands still for 10s.
4. The object moves away from the origin at a steady
speed for 10s, reverses direction and moves back
toward the origin at the same speed.
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Draw the velocity vs time graphs for an object whose motion produced the position vs time graphs shown
below at left.
5.
6.
7.
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UNIT II READING: MOTION MAPS
A motion map represents the position, velocity, and acceleration of an object at various clock readings.
(At this stage of the class, you will be representing position and velocity only.)
Suppose that you took a stroboscopic picture of a car moving to the right at constant velocity where each
image revealed the position of the car at one-second intervals.
This is
the motion map that represents the car. We model the position of the object with a small point. At each
position, the object's velocity is represented by a vector.
If the car were traveling at greater velocity, the strobe photo might look like this:
The corresponding motion map has the points spaced farther apart, and the velocity vectors are longer,
implying that the car is moving faster.
If the car were moving to the left at constant velocity, the photo and motion map might look like this:
More complicated motion can be represented as well.
Here, an object moves to the right at constant velocity, stops and remains in place for two seconds, then
moves to the left at a slower constant velocity.
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Consider the interpretation of the motion map below. At time t = 0, cyclist A starts moving to the right at
constant velocity, at some position to the right of the origin.
Cyclist B starts at the origin and travels to the right at a constant, though greater velocity.
At t = 3 s, B overtakes A (i.e., both have the same position, but B is moving faster).
A graphical representation of the behavior of cyclists A and B would like this:
You could also represent the behavior algebraically as follows:
x  v At  x0 , for A
x  v Bt,
for B
where vB > vA
Throughout this semester, you will be representing the behavior of objects in motion in multiple ways:
diagrammatically (motion maps), graphically and algebraically.
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UNIT II: Worksheet 4
1. From the motion map above, answer the following:
a. What can you conclude about the motion of the object?
b. Draw a qualitative graphical representation of x vs t (see below).
c. Draw a qualitative graphical representation of v vs t (see below).
x
v
t
t
fig. 1
fig. 2
d. Write a mathematical expression that represents the relationship between x and t, from fig. 1.
e. Write a mathematical expression that represents the relationship between v and t, from fig. 2
f. Describe what the area under the curve in fig. 2 represents. Cross hatch this area.
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2. From the position vs time data below, answer the following questions.
t (s)
0
1
2
3
4
5
6
7
8
9
x (m)
0
2
4
4
7
10
10
10
5
0
a. Construct a graph of position vs time.
b. Construct a graph of velocity vs time.
c. Draw a motion map for the object.
d. Determine the displacement from t = 3.0s to 5.0s using graph B.
e. Determine the displacement from t = 7.0 s to 9.0 s using graph B.
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UNIT II: Worksheet 5
1
2
4
x
x vs. t graph
x
3
t
Motion Map
Written Description
v vs. t graph
t
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7
Object moves with
constant positive
velocity for 4 seconds.
Then, it stops for 2
seconds and returns to
the initial position in 2
seconds.
Object A starts 10m to
the right of the origin
and moves to the left at
2 m/s.
Object B starts at the
origin and moves to the
right at 3m/s.
Motion Map
Written Description
v vs. t graph
x vs. t graph
5
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