Name: _____________________________________________
Period: _____
Unit I: Motion
Subunit A: Constant Velocity
Chapter 2 Section 1 Texas Physics p. 38-45
Equations
Variables, Units
NOTES:
Unit I-A Objectives
What you should know when all is said and done
1. You should distinguish between a scalar and a vector:
a. know the difference between distance and displacement.
b. know the difference between speed and velocity.
c. know the difference between average and instantaneous speed and velocity.
2. You should be able to determine the average velocity of an object in two ways:
a. determining the slope of an x vs t graph.
b. using the equation v = Δx/Δt
3. You should be able to determine the displacement of an object in two ways:
a. finding the area under a v vs t graph.
b. using the equation Δx = vt
4. Given an x vs t graph, you should be able to:
a. describe the motion of the object (starting position, direction of motion, velocity)
b. draw the corresponding v vs t graph
c. determine the average velocity of the object (slope).
d. write the mathematical model which describes the motion.
5. Given a v vs t graph, you should be able to:
a. describe the motion of the object (direction of motion, how fast)
b. draw the corresponding x vs t graph
c. determine the displacement of the object (area under curve).
d. write a mathematical model to describe the motion.
Unit I-A: Constant Velocity
Worksheet 1
(refer to p.82 Texas Physics for intro to scalar and vector)
1. When choosing a 1-dimensional horizontal reference frame, or coordinate system, we
usually choose the positive direction to be toward the (right / left) and the negative direction to
be toward the (right / left).
2. ______ A quantity that only describes how much (magnitude) is referred to as a
A) scalar quantity
B) vector quantity
3. ______ A quantity that describes how much (magnitude) and which way (direction) is referred
to as a
A) scalar quantity
B) vector quantity
3. Some examples of scalars are:
4. Some examples of vectors are:
5. To measure displacement, or change in position Δx,
A) measure every meter moved
B) take the final position minus the initial position only
6. True or False: An object can be moving for 10 seconds and still have zero displacement.
7. True or False: It is possible for an object to move for 10 seconds at a high speed and end up
with negative displacement.
8. Johnny drives to 1920 miles in 32 hours and returns home by the same route in the same
amount of time.
A) Determine his average speed.
B) Determine his average velocity.
C) Compare these two values and explain any differences.
questions.
8.
This person walks a distance of ________ km.
9.
This person has a displacement of ________ km.
a. 0 km
b. 3 km
c. 3 km, E
d. 3 km, W
e. 5 km
f. 5 km, N g. 5 km, S
h. 6 km
i. 6 km, E j. 6 km, W k. 31 km
l. 31 km, E
m. 31 km, W
n. None of these.
9. AAcross-country
skiermoves
movesfrom
from
location
A location
to location
to location
C to location
D.leg
Each
leg
10.
cross-country skier
location
A to
B toBlocation
C to location
D. Each
of the
of the
back-and-forth
motion
1 minute
to complete;
total
is 3 minutes.
back-and-forth
motion
takestakes
1 minute
to complete;
the totalthe
time
is 3time
minutes.
A) What
is the
distance
skierduring
duringthe
thethree
three
minutes
of recreation?
a. What
is the
distancetraveled
traveled by
by the skier
minutes
of recreation?
b. What is the net displacement of the skier during the three minutes of recreation?
B) What is the net displacement of the skier during the three minutes of recreation?
c. What is the displacement during the second minute (from 1 min. to 2 min.)?
C) What is the displacement during the second minute (from 1 min. to 2 min.)?
d. What is the displacement during the third minute (from 2 min. to 3 min.)?
D) What is the displacement during the third minute (from 2 min. to 3 min.)?
E) Calculate the average speed (in m/min) and the average velocity (in m/min) of the skier
during the three minutes of recreation.
© The Physics Classroom, 2009
Page 2
10.
Position (m)
A) Equation: _______________________
10
B) This object starts ______ meters away from the origin
and travels with a ______________ ______________ in
the (+ / - ) direction, (away from/towards) the origin, for
10 seconds at a speed of ____________.
0
0
10
Time (s)
11.
Position (m)
10
A) Equation:
B) This object starts ______ meters away from the
origin and travels with a ______________
______________ in the (+ / - ) direction, (away
from/towards) the origin, for 10 seconds at a speed of
____________.
0
0
10
Time (s)
12.
0
10
Time (s)
A) Equation:
B) Describe the motion of this object as above.
-10
Position (m)
Unit I-A: Constant Velocity
Worksheet 2
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?
x
(m)
A
B) At t = 7 s, which cyclist is ahead? How do
you know?
B
C) Which cyclist is traveling faster at t = 3 s?
How do you know?
5
t (s)
D) Are their velocities equal at any time? How do you know?
E) What is happening at the intersection of line A and B?
2. Consider the position vs. time graph below for cyclists A and B.
2. Consider the position vs. time graph below for cyclists A and B.
X (m)
A
A) How does the motion of the two cyclists in
this graph compare to the previous question?
B
B) Which cyclist has the greater speed?
How do you know?
5
t (s)
a. How does the motion of the cyclist A in this graph compare to that of A in the previous graph
C) on
Which
cyclist has traveled further during the first 5 seconds? How do you know?
page one?
b. How does the motion of cyclist B in this graph compare to that of B in the previous graph on
page one?
c. Which cyclist has the greater speed? How do you know?
3. A) Using the Data Table below, create a graph and write the corresponding equation
Time
(s)
0
1
Position
(m)
15
12
2
9
3
4
6
3
5
0
A) Find the equation of the line.
B) Describe the motion of the object.
4. The graph at below shows the motion of a girl on a jet ski moving in a straight line.
A) What is the total distance she travels?
B) What is her total displacement?
C) What is her average speed?
D) What is her average velocity?
Unit I-A: Constant Velocity
Worksheet 3
1. A motorized scooter was observed to be at the following positions at the times listed below:
t (s)
x (m)
0
11
A) Plot the position vs. time graph
1
9
for the scooter.
2
7
3
5
B) Was the scooter’s velocity
4
3
constant throughout the
5
1
whole interval? How do you know?
C) What is the velocity of the scooter? Show work.
D) What would his position be at t = 7 s if his velocity
remains constant? Use your equation to find out.
2. Robin, roller-skating down a sidewalk, was observed to be at the following positions at the
times listed below:
t (s)
x (m)
0
2
A) Plot a position vs. time graph for
1
5
the skater.
2
8
4
14
6
20
8
26
B) Find the velocity of the skater.
C) What is the equation that models her motion?
D) How far from the origin was she at t = 5 s? Show work.
E) What would be her position at t = 12 seconds if her velocity remains constant? Show work.
3. The following data were obtained for the skater’s second trial:
t (s)
0
2
4
6
8
10
x (m)
4
10
16
22
28
34
A) Plot the position vs. time graph
for the skater.
B) Find the velocity of the skater.
C) What is the equation that models her motion?
D) How far from the origin was she at t = 5 s?
E) What would be her position at t = 12 seconds if her velocity remains constant?
4. A spider runs back and forth in a straight line with the following data obtained:
t (s)
x (m)
0
4
A) Plot the position vs. time graph for
2
6
the spider.
4
12
6
12
8
8
10
4
12
0
B) What do you think is happening during the time interval:
t = 4s to t = 6 s? How do you know?
C) What do you think is happening during the time interval
t = 6s to t = 12s? How do you know?
D) Determine the spider’s average speed from t = 0s to t = 12s.
E) Determine the spider’s average velocity from t = 0s to t = 12s.
5. The spider is now seen to move in the following manner:
t (s)
x (m)
0
8
A) Plot the position vs. time graph for
2
7
the spider.
4
6
6
8
10
12
6
8
10
12
B) During what time interval is the spider traveling the
fastest? How do you know?
C) What do you think is happening during the time interval
t = 4s to t = 6 s? How do you know?
D) Determine the spider’s average speed from t = 0s to t = 12s.
E) Determine the spider’s average velocity from t = 0s to t = 12s.
6. This data table shows information about two toy cars that were raced side-by-side.
t (s)
0
1
2
3
4
5
6
7
8
9
10
x1 (m)
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
x2 (m)
0
1
2
3
4
5
6
7
8
9
10
A) Draw a graph of both
cars on the same graph.
B) Find the velocity of each toy car. Show your work.
Unit I-A: Constant Velocity
Worksheet 4
1. Use the table below to answer the following questions.
t (s)
0
1
2
3
4
x (m)
2
4
6
8
10
A) Draw position-time and velocity-time graphs for the object on the graphs
below.
Position (m)
Velocity (m/s)
Time (s)
Time (s)
B) Write mathematical expressions that represent the relationships between position and time
and between velocity and time for the object.
C) Describe what the area under the line in velocity-time graph represents. Crosshatch this area.
2. Use the position-time data below to 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 position vs. time graph and a velocity vs. time graph for
this data.
Position (m)
Velocity (m/s)
Time (s)
14
Time (s)
B) Determine the displacement from t = 3.0 s to 5.0 s using the velocity-time graph. Show on
the graph what you did and explain your thinking.
C) Determine the displacement from t = 7.0 s to 9.0 s using the velocity-time graph. Show on
the graph what you did and explain your thinking.
D) Compare your results to the position-time graph. Do the two results match?
Unit I-A: Constant Velocity
Worksheet 5
1. Sketch the position vs. time graph and the velocity vs. time graph corresponding to the
following descriptions of the motion of an object.
A) The object is moving away from the origin at a
constant (steady) speed.
B) The object is standing still.
C) The object moves towards the origin at a steady speed,
then it stands still.
D) The object moves away from the origin at a steady speed,
then reverses direction and moves back towards the origin at
the same speed.
Draw
the velocity
vs time
graphs
for for
an an
object
whose
motion
produced
the
vsvs.
time
graphs
2. Draw
the velocity
vs. time
graph
object
whose
motion
produced
theposition
distance
time
shownshown
below below
at left.at left.
graphs
5.
6.
7.
8. For many graphs, both the slope of the line and the area between the line and the horizontal axis
have
meanings.
3.
For physical
many graphs,
both the slope of the line and the area between the line and the horizontal
a. What
doesphysical
the slope
of a position time graph tell you about the motion of an object?
axis have
meanings.
A) What does the slope of a position time graph tell you about the motion of an object?
b. Looking at the velocity time graphs, determine the units for a square of area on the graph.
B) Looking at the velocity time graphs, determine the units for a square of area on the graph.
c. What
does
the the
areaarea
under
the the
velocity-time
graph
tell
C) What
does
under
velocity-time
graph
tellyou
youabout
aboutthe
themotion
motionof
of an
an object?
object?
©Modeling Instruction Program 2009
5
Constant Velocity ws2
x
t
Unit I-A: Constant Velocity
Worksheet 6
v
Motion map:
Fill in the blank boxes with the correct complete information.
Constant Velocity Particle Model Worksheet t4:
Multiple Representations of Motion
x - t Graph
v - t Graph
Written Description
Given one motion representation, supply the missing motion representations.
1.
Written description:
x
2.
The object starts at 2m and
moves with a constant
positive velocity for two
Written
description:
seconds,
then
stops for 2s,
then returns past the
starting point at a faster
speed in 2s.
x
3.
t
Written description:
x
v
t
Motion map:
t
v
Motion map:
3
6
8
t (s)
t
v
2.
Motion map:
Written description:
t
x
3.
Written description:
x
4.
t
Written description:
x
v
3
6
8
t (s)
t
v
Motion map:
Motion map:
t
t
+2
Motion map:
v
(m/s)
-1
4.
2
4
Written description:
x
t
+2
v
Motion map:
8 t (s)
x - t Graph
v - t Graph
Written Description
The object moves with a
constant positive velocity for
4 seconds. Then, it
stops for 2 seconds and
returns to the initial position
in 2 seconds.
The object starts 5m away
from the origin and moves
towards the origin with a
constant velocity for 2
seconds. Then it stops at
1m from the origin for 2
seconds. Then it turns
around and moves away
from the origin with half the
velocity for 4 seconds.
Object A starts 10m to the
right of zero and moves to
the left at 2m/s.
Object B starts at zero and
moves to the right at 3 m/s
Object A starts at the origin
and moves with a constant
positive velocity for 5
seconds. Object B starts 1m
away from the origin and
moves with the same
constant velocity as object
A.
Unit I-A: Constant Velocity
Review Worksheet
(Also, practice 1-6 p.42 and 1-6 p.45 Texas Physics)
Constant V
Vocabulary Terms
Coordinate System
Displacement
Distance
Scalar Quantity
Vector Quantity
Frame of reference
Average Velocity
Average Speed
Instantaneous Velocity
Re
1. Consider the following position vs. tim
Review Problems
a. Det
1. Consider the position vs. time graph shown.
A) Determine the average velocity of the object.
b. Wr
ob
B) Write the mathematical equation to describe the motion of the
object.
C) Using the equation for the graph, find the position of the object at
t = 10 s.
2. Consider the following v vs. t graph.
A) Describe the behavior of the object.
2. Shown below is a velocity vs. time grap
4. A basketball initially travels at 3 meters
a. Describ
B) Draw a position vs. time graph to model the behavior of the
object.
b. Draw a corresponding position vs. time
from
the origin.
b. Draw
a quantitative motion map that m
C) How far did the object travel in the interval t = 1s to t = 2s?
0m
c. H
D) What is the TOTAL displacement? Explain how you got your answer.
c. How far did the ball travel from t = 3s t
d. F
3. The following graph depicts the motion of a bee going from flower to flower.
Position (m)
10
8
6
4
2
0
0
2
4
6
8
10
12
14
Time (s)
A) What distance was traveled between time 2 s and time 6 s? What was the displacement?
B) What was the speed between times 2 s and 6 s? What was the velocity?
C) What is the distance traveled between time 4 s and time 12 s? What was the displacement?
D) What was the average speed between time 4 s and time 12 s? What was the average
velocity over this time frame?
E) What is the total distance traveled? Total displacement? Average speed? Average velocity?
4. A racecar travels at a speed of 95 m/s. How much time does it take to reach the finish line
500 m away?
5. A hummingbird averages a speed of about 28 miles/hour (Cool facts: They visit up to 1000
flowers per day, and reach maximum speed while diving ... up to 100 miles/hour!). Rubythroated hummingbirds take a 2000-mile journey when they migrate, including a non-stop trip
across Gulf of Mexico in which they fly for 18 hours straight! How far is the trip across the Gulf
of Mexico?
6. Dr. Foster and Mr. Padilla are out skateboarding. The table shows their motion over time.
Use the table to answer the questions.
Time
(s)
Position
Dr. Foster
(m)
Position
Mr. Padilla
(m)
0
0
45
5
10
40
10
20
35
15
30
30
20
40
25
25
50
20
30
60
15
A) Draw a position-time graph for each skateboarder.
Position (m)
Time (s)
B) Does either one of the administrators move at a constant velocity? How do you know?
C) Do Dr. Foster and Mr. Padilla move in the same direction? How do you know?
D) What is happening at time = 15s?
E) How fast is Dr. Foster going? How fast is Mr. Padilla going? Show your work.