Chapter 2
Describing Motion
Chapter 2: Describing Motion
Reading Assignment
Read Sections 3.1–3.3
Homework Assignment 1
Homework for Chapters 1 and 2 (due Tuesday, August 31)
Chapter 1: Q2, Q14, Q18, E4, E12
Chapter 2: Q4, Q16, Q18, Q30, E8, E14, E18
Note
Friday office hours have been changed to 10:30–12:00
Chapter 2: Describing Motion
Average speed
An object’s average speed is equal to the distance it traveled divided by the time of travel
s =
d
t
In other words, average speed is the rate at which distance is covered over time
Instantaneous speed
An object’s instantaneous speed (sometimes called its speed) is found by computing its average speed for a very
short time interval during which the speed does not change by an appreciable amount
Chapter 2: Describing Motion
Average speed
An object’s average speed is equal to the distance it traveled divided by the time of travel
s =
d
t
In other words, average speed is the rate at which distance is covered over time
Instantaneous speed
An object’s instantaneous speed (sometimes called its speed) is found by computing its average speed for a very
short time interval during which the speed does not change by an appreciable amount
Scalars
Both average speed and instantaneous speed are examples of scalar quantities
Scalar quantities have just a magnitude (a size)
Other examples of scalar quantities include temperature, mass and energy
Chapter 2: Describing Motion
Average speed
An object’s average speed is equal to the distance it traveled divided by the time of travel
s =
d
t
In other words, average speed is the rate at which distance is covered over time
Instantaneous speed
An object’s instantaneous speed (sometimes called its speed) is found by computing its average speed for a very
short time interval during which the speed does not change by an appreciable amount
Scalars
Both average speed and instantaneous speed are examples of scalar quantities
Scalar quantities have just a magnitude (a size)
Other examples of scalar quantities include temperature, mass and energy
Question
What are the units for speed?
Chapter 2: Describing Motion
Position
An object’s position is its location relative to some reference point
Average velocity
An object’s average velocity is equal to the change in its position divided by the time required to produce that
change
−
∆→
x
→
−
v =
t
Instantaneous velocity
An object’s instantaneous velocity (sometimes called its velocity) has a magnitude that is equal to its
instantaneous speed at a given instant in time and has a direction that corresponds to the object’s motion at that
instant
Chapter 2: Describing Motion
Position
An object’s position is its location relative to some reference point
Average velocity
An object’s average velocity is equal to the change in its position divided by the time required to produce that
change
−
∆→
x
→
−
v =
t
Instantaneous velocity
An object’s instantaneous velocity (sometimes called its velocity) has a magnitude that is equal to its
instantaneous speed at a given instant in time and has a direction that corresponds to the object’s motion at that
instant
Vectors
Position, average velocity and instantaneous velocity are examples of vector quantities
Vector quantities have a magnitude and a direction
Other examples of vector quantities include force and momentum
Chapter 2: Describing Motion
Position
An object’s position is its location relative to some reference point
Average velocity
An object’s average velocity is equal to the change in its position divided by the time required to produce that
change
−
∆→
x
→
−
v =
t
Instantaneous velocity
An object’s instantaneous velocity (sometimes called its velocity) has a magnitude that is equal to its
instantaneous speed at a given instant in time and has a direction that corresponds to the object’s motion at that
instant
Vectors
Position, average velocity and instantaneous velocity are examples of vector quantities
Vector quantities have a magnitude and a direction
Other examples of vector quantities include force and momentum
Question
What does a car’s speedometer measure?
Chapter 2: Describing Motion
Question
At the 2008 Beijing Olympics, Michael Phelps set a World Record in the 200 m butterfly, swimming the event in
1:52.03 (= 112.03 s). What was his average speed for the entire event?
Chapter 2: Describing Motion
Question
At the 2008 Beijing Olympics, Michael Phelps set a World Record in the 200 m butterfly, swimming the event in
1:52.03 (= 112.03 s). What was his average speed for the entire event?
Answer
His average speed for the entire event was
s =
Chapter 2: Describing Motion
d
t
=
200 m
112.03 s
= 1.79 m/s
Question
At the 2008 Beijing Olympics, Michael Phelps set a World Record in the 200 m butterfly, swimming the event in
1:52.03 (= 112.03 s). What was his average velocity for the entire event?
Chapter 2: Describing Motion
Question
At the 2008 Beijing Olympics, Michael Phelps set a World Record in the 200 m butterfly, swimming the event in
1:52.03 (= 112.03 s). What was his average velocity for the entire event?
Answer
His average velocity for the entire event was
−
0m
∆→
x
→
−
=
= 0 m/s
v =
t
112.03 s
Chapter 2: Describing Motion
Acceleration
Acceleration is the rate at which velocity changes
Acceleration is a vector quantity
Average acceleration
An object’s average acceleration is the equal to the change in its velocity divided by the time required to produce
that change
−
∆→
v
→
−
a =
t
Instantaneous acceleration
An object’s instantaneous acceleration is found by computing its average acceleration for a very short time interval
during which its acceleration does not appreciably change
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed.
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt.
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car.
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor.
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor. Yes (up)
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor. Yes (up)
An elevator that is stopping at the fifth floor.
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor. Yes (up)
An elevator that is stopping at the fifth floor. Yes (down)
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor. Yes (up)
An elevator that is stopping at the fifth floor. Yes (down)
An elevator that is moving up at constant speed.
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor. Yes (up)
An elevator that is stopping at the fifth floor. Yes (down)
An elevator that is moving up at constant speed. No
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor. Yes (up)
An elevator that is stopping at the fifth floor. Yes (down)
An elevator that is moving up at constant speed. No
A car going up a hill at constant speed.
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor. Yes (up)
An elevator that is stopping at the fifth floor. Yes (down)
An elevator that is moving up at constant speed. No
A car going up a hill at constant speed. No
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor. Yes (up)
An elevator that is stopping at the fifth floor. Yes (down)
An elevator that is moving up at constant speed. No
A car going up a hill at constant speed. No
A car going going at constant speed around a corner.
Chapter 2: Describing Motion
The direction of acceleration
Acceleration points in the same direction you would have to pull to obtain the change in velocity
Question
Can an object be accelerating when its speed is constant?
Remember
Velocity is a vector. Therefore, if either its magnitude or its direction changes, there is an acceleration.
Some examples
Is there an acceleration and, if so, what direction is it in?
A car picking up speed. Yes (forward)
A car skidding to a halt. Yes (backward)
A parked car. No
An elevator that begins moving from the first floor to the fifth floor. Yes (up)
An elevator that is stopping at the fifth floor. Yes (down)
An elevator that is moving up at constant speed. No
A car going up a hill at constant speed. No
A car going going at constant speed around a corner. Yes (we will discuss this later)
Chapter 2: Describing Motion
In mechanics, the three basic quantities are . . .
Quantity
SI Unit
Abbreviation
Position
meter
m
Mass
kilogram
kg
Time
second
s
Advantage of using the SI system
Different units for the same quantity are related by factors of 10. (e.g. the prefix kilo- means 1000, so a kilogram
is a 1000 grams and a kilometer is a 1000 meters)
Some more units . . .
Quantity
SI Unit
Velocity
meter-per-second
Acceleration
Chapter 2: Describing Motion
Abbreviation
2
meter-per-second
m/s
m/s2
Question
What was the average acceleration when Eli Beeding Jr. reached 72.5 mi/h in 0.040 s on a rocket sled?
Chapter 2: Describing Motion
Question
What was the average acceleration when Eli Beeding Jr. reached 72.5 mi/h in 0.040 s on a rocket sled?
Answer
Acceleration is the change in velocity over time so
a=
Chapter 2: Describing Motion
72.5 mi/h − 0 mi/h
0.040 s
≈ 1800 mi/h · s
Question
What was the average acceleration when Eli Beeding Jr. reached 72.5 mi/h in 0.040 s on a rocket sled?
Answer
Acceleration is the change in velocity over time so
a=
72.5 mi/h − 0 mi/h
0.040 s
≈ 1800 mi/h · s
Or we could convert to SI units . . .
Conversion:
1 mi = 5280 ft
Chapter 2: Describing Motion
and
1 m = 3.28 ft
Question
What was the average acceleration when Eli Beeding Jr. reached 72.5 mi/h in 0.040 s on a rocket sled?
Answer
Acceleration is the change in velocity over time so
a=
72.5 mi/h − 0 mi/h
0.040 s
≈ 1800 mi/h · s
Or we could convert to SI units . . .
Conversion:
1 mi = 5280 ft
Therefore
1800 mi/h · s
Chapter 2: Describing Motion
and
1 m = 3.28 ft
Question
What was the average acceleration when Eli Beeding Jr. reached 72.5 mi/h in 0.040 s on a rocket sled?
Answer
Acceleration is the change in velocity over time so
a=
72.5 mi/h − 0 mi/h
0.040 s
≈ 1800 mi/h · s
Or we could convert to SI units . . .
Conversion:
1 mi = 5280 ft
and
Therefore
1800 mi/h · s = 1800 mi/h · s
Chapter 2: Describing Motion
5280 ft
1 mi
1 m = 3.28 ft
Question
What was the average acceleration when Eli Beeding Jr. reached 72.5 mi/h in 0.040 s on a rocket sled?
Answer
Acceleration is the change in velocity over time so
a=
72.5 mi/h − 0 mi/h
0.040 s
≈ 1800 mi/h · s
Or we could convert to SI units . . .
Conversion:
1 mi = 5280 ft
and
1 m = 3.28 ft
Therefore
1800 mi/h · s = 1800 mi/h · s
Chapter 2: Describing Motion
5280 ft
1 mi
1m
3.28 ft
Question
What was the average acceleration when Eli Beeding Jr. reached 72.5 mi/h in 0.040 s on a rocket sled?
Answer
Acceleration is the change in velocity over time so
a=
72.5 mi/h − 0 mi/h
0.040 s
≈ 1800 mi/h · s
Or we could convert to SI units . . .
Conversion:
1 mi = 5280 ft
and
1 m = 3.28 ft
Therefore
1800 mi/h · s = 1800 mi/h · s
Chapter 2: Describing Motion
5280 ft
1 mi
1m
3.28 ft
1h
3600 s
Question
What was the average acceleration when Eli Beeding Jr. reached 72.5 mi/h in 0.040 s on a rocket sled?
Answer
Acceleration is the change in velocity over time so
a=
72.5 mi/h − 0 mi/h
0.040 s
≈ 1800 mi/h · s
Or we could convert to SI units . . .
Conversion:
1 mi = 5280 ft
and
1 m = 3.28 ft
Therefore
1800 mi/h · s = 1800 mi/h · s
Chapter 2: Describing Motion
5280 ft
1 mi
1m
3.28 ft
1h
3600 s
2
≈ 800 m/s
Question
How would you plot the motion of the cart on the air track on a Position v. Time graph?
Chapter 2: Describing Motion
Question
How would you plot the motion of the cart on the air track on a Position v. Time graph?
Position v. Time
The slope of a Position v. Time curve indicates how rapidly the position is changing with time at any
instant
The slope of this curve at any point on the graph is equal to the instantaneous velocity of the object at
that point
Chapter 2: Describing Motion
Question
How would you plot the motion of the cart on the air track on a Position v. Time graph?
How about on a Velocity v. Time graph?
Position v. Time
The slope of a Position v. Time curve indicates how rapidly the position is changing with time at any
instant
The slope of this curve at any point on the graph is equal to the instantaneous velocity of the object at
that point
Chapter 2: Describing Motion
Question
How would you plot the motion of the cart on the air track on a Position v. Time graph?
How about on a Velocity v. Time graph?
Position v. Time
The slope of a Position v. Time curve indicates how rapidly the position is changing with time at any
instant
The slope of this curve at any point on the graph is equal to the instantaneous velocity of the object at
that point
Velocity v. Time
The slope of a Velocity v. Time curve indicates how rapidly the velocity is changing with time at any
instant
The slope of this curve at any point on the graph is equal to the instantaneous acceleration of the object
at that point
The change in position of an object can be found from a Velocity v. Time curve by finding the area under
the curve
Chapter 2: Describing Motion
Question
How would you plot the motion of the cart on the air track on a Position v. Time graph?
How about on a Velocity v. Time graph?
An Acceleration v. Time graph?
Position v. Time
The slope of a Position v. Time curve indicates how rapidly the position is changing with time at any
instant
The slope of this curve at any point on the graph is equal to the instantaneous velocity of the object at
that point
Velocity v. Time
The slope of a Velocity v. Time curve indicates how rapidly the velocity is changing with time at any
instant
The slope of this curve at any point on the graph is equal to the instantaneous acceleration of the object
at that point
The change in position of an object can be found from a Velocity v. Time curve by finding the area under
the curve
Chapter 2: Describing Motion
Questions
If you are coasting in a car traveling to the right, how would observers on the sidewalk describe your
motion?
Chapter 2: Describing Motion
Questions
If you are coasting in a car traveling to the right, how would observers on the sidewalk describe your
motion? You are traveling to the right with constant speed
Chapter 2: Describing Motion
Questions
If you are coasting in a car traveling to the right, how would observers on the sidewalk describe your
motion? You are traveling to the right with constant speed
How would you describe their motion?
Chapter 2: Describing Motion
Questions
If you are coasting in a car traveling to the right, how would observers on the sidewalk describe your
motion? You are traveling to the right with constant speed
How would you describe their motion? They are traveling to the left at the same speed
Chapter 2: Describing Motion
Questions
If you are coasting in a car traveling to the right, how would observers on the sidewalk describe your
motion? You are traveling to the right with constant speed
How would you describe their motion? They are traveling to the left at the same speed
Who is right?
You are both right!
Chapter 2: Describing Motion
Questions
If you are coasting in a car traveling to the right, how would observers on the sidewalk describe your
motion? You are traveling to the right with constant speed
How would you describe their motion? They are traveling to the left at the same speed
Who is right?
You are both right!
Physics Concept: Inertial Frame of Reference
Inertial Frame of Reference: a reference frame (viewpoint) that is not accelerating
Chapter 2: Describing Motion
Questions
If you are coasting in a car traveling to the right, how would observers on the sidewalk describe your
motion? You are traveling to the right with constant speed
How would you describe their motion? They are traveling to the left at the same speed
Who is right?
You are both right!
Physics Concept: Inertial Frame of Reference
Inertial Frame of Reference: a reference frame (viewpoint) that is not accelerating
Why are they important?
Observers in different frames of reference may disagree about particular measure quantities (e.g velocity) but
the laws of physics work just fine in any inertial frame of reference!
Chapter 2: Describing Motion
Reading Assignment
Read Sections 3.1–3.3
Homework Assignment 1
Homework for Chapters 1 and 2 (due Tuesday, August 31)
Chapter 1: Q2, Q14, Q18, E4, E12
Chapter 2: Q4, Q16, Q18, Q30, E8, E14, E18
Note
Friday office hours have been changed to 10:30–12:00
Chapter 2: Describing Motion