Motion in One Dimension
Chapter 2
Holt Physics
2-1 Displacement and Velocity
• Essential Questions / Concepts
• Describe motion in terms of frame of
reference, displacement, time, and velocity.
• Calculate the displacement of an object
traveling at a known velocity for a specific
time interval.
• Construct and interpret graphs of position
versus time.
One Dimensional Motion
• One dimensional motion is the simplest form.
• It is motion that only takes place in a straight
line.
• In can include motion in two directions (left
and right, forward and back…)
Frame of Reference
• One must choose a frame of reference to
describe any form of motion.
• If an object is at rest (not moving), its position
does not change with respect to the frame of
reference.
• Any frame of reference will do as long as we
are consistent.
Displacement
• The length of a straight line drawn from an
object’s initial position to its final position.
• Displacement = change in position =
Final position – initial position
Δx = xf – xi
Displacement
• Displacement is not always equal to the
distance traveled.
• Displacement can be positive or negative.
– Unless otherwise stated, movement to the right or
upward movement will be considered positive
– Movement to the left or downward movement
will be considered negative.
Velocity
• Average velocity is displacement divided by the
time interval.
• The unit of velocity is meters per second, or m/s
Δx
V avg =
xf - x i
=
Δt
tf - ti
Average Velocity
• Average velocity can be either positive or
negative depending on the sign of the
displacement.
• Average velocity is equal to the constant
velocity needed to cover the displacement in
the given time interval.
Problems: Page 44
#1 Heather and Matthew walk eastward with
a speed of 0.98 m/s. If it takes the 34 minutes
to walk to the store, how far have they
walked?
North = 0 Degrees or 360 Degrees
West = 270
Degrees
East = 90
Degrees
South = 180 Degrees
Problems: Page 44
#2 If Joe rides south on his bicycle in a straight
line for 15 minutes with an average speed of
12.5 km/h, how far has he riden?
Problems: Page 44
#3 It takes you 9.5 min to walk with an
average velocity of 1.2 m/s to the north from
the bus stop to the museum entrance. What is
your displacement?
Problems: Page 44
#4 Simpson drives his car with an average
velocity of 48.0 km/h to the east. How long
will it take him to drive 144 km on a straight
highway?
Problems: Page 44
#5 Look back at item #4. How much time
would Simpson save by increasing his average
velocity to 56.0 km/h to the east?
Problems: Page 44
#6 A bus travels 280 km south along a straight
path with an average velocity of 88 km/h to
the south. The bus stops for 24 min, then it
travels 210 km south with an average velocity
of 75 km/h to the south.
a) How long does the total trip last?
b) What is the average velocity for the total
trip?
Velocity vs Speed
• Velocity describes motion with both a
direction and a numerical value (a
magnitude).
• Speed has no direction, only a magnitude.
Interpreting Velocity Graphically
• Velocity is a graph of change in position vs
change in time.
• Position is on the y-axis while time is on the xaxis.
• The slope of the line (rise over run) is equal to
the velocity (meters per second).
Position (m)
Graphing Velocity
Object #1
Object #2
Object #3
Time (s)
Average vs Instantaneous Velocity
Position (m)
Describe the average velocity:
Where is average velocity equal to
Instantaneous velocity?
Time (s)
Average vs Instantaneous Velocity
Position (m)
Describe the average velocity:
Where is average velocity equal to
Instantaneous velocity?
Time (s)
Average vs Instantaneous Velocity
• Instantaneous velocity may not be the same
as the average velocity.
• To determine instantaneous velocity we must
consider a small (VERY small) time interval.
• A straight line that is TANGENT to the curve of
velocity indicates instantaneous velocity.
Position (m)
Consider Problem 3 on Page 47
Time (s)
Number 5, Page 47
• An athlete swims from the north end to the
south end of a 50.0 m pool in 20.0 s and
makes the return trip to the starting position
in 22.0 s.
– What is the average velocity of the first half?
– What is the average velocity for the second half?
– What is the average velocity for the round trip?
Number 6, Page 47
• Two students walk in the same direction along
a straight path, at a constant speed – one at
0.90 m/s and the other at 1.90 m/s.
– Assuming that they start at the same point at the
same time, how much sooner does the faster
student arrive at a destination 780 m away?
– How far would the student have to walk so that
the faster student arrives 5.50 min before the
slower student?
2-2 Acceleration
• Essential Questions / Concepts:
• Describe motion in terms of changing velocity.
• Compare graphical representations of
accelerated and non-accelerated motions.
• Apply kinematic equations to calculate
distance, time, or velocity under conditions of
constant acceleration.
Changes in Velocity
• Acceleration measures the rate of change in
velocity.
• What is on the x-axis of any graph of a rate?
• A graph of acceleration is a graph of velocity
over time (meters per second, per second).
Acceleration
• Average acceleration is velocity divided by the
time interval.
• The unit of acceleration is meters per second per
second , or m/s2
Δv
aavg =
v f - vi
=
Δt
tf - ti
Problems 1-5 on Page 49
• Homework assignment – you
MUST show your work!
Changes in Velocity
• Acceleration has both direction and
magnitude.
• When the Δv is positive, the acceleration is
positive.
• When the velocity is constant, the
acceleration is equal to zero.
Changes in Velocity
• Imagine a train, traveling in a positive
direction, slows down as it approaches the
next station.
• Is the acceleration positive or negative?
• Acceleration is final velocity minus initial
velocity, so the Δv will be negative and the Δa
will be negative even though the velocity is
always positive.
Slope and Shape of Graph of Motion
Describe in detail the motion at each of the
three marked points
Motion with Constant Acceleration
Velocity vs Time (Acceleration) for Giancarlo Fiscichella at Melbourne, Australia
Displacement
• Displacement depends on acceleration, initial
velocity, and time.
• The area under the curve in a graph of velocity
versus time equals the displacement.
Equation for Displacement with
Constant Acceleration
Look at the sample problem on page 53…
Do Problems 1-5 on page 53 for homework.
Final Velocity
• Final velocity depends on initial velocity,
acceleration, and time.
• By rearranging the equation for acceleration,
we can find a value for the final velocity.
Equation for Final Velocity with
Constant Acceleration
Another Equation for Displacement
with Constant Acceleration
Look at the sample problem on page 55…
Do Problems 1-4 on page 55 for homework.
Equation for Final Velocity
2-3 Falling Objects
• Essential Questions / Concepts
• Relate the motion of a freely falling body to
motion with constant acceleration.
• Calculate displacement, velocity, and time at
various points in the motion of a freely falling
object.
• Compare the motions of different objects in
free fall
Free Fall
• It has been demonstrated that in the absence
of air resistance all objects fall with the same
constant acceleration.
• Free fall acceleration is denoted by the symbol
g.
• The acceleration of all objects near the earth’s
surface is approximately 9.81 m/s2.
Constant Free Fall Acceleration
The graph indicates constant
acceleration at every moment
To Summarize Motion
Homework Problems
• Students should understand and be able to
answer the Review Questions from each section
on pages 69-72.
• From the Chapter 3 Review and Assess section
beginning on page 69 do problem numbers 8, 10,
14, 20, 24, 26, 30,38, 40, and 42.
• Bonus Questions for Extra Credit: number 45, 46,
55 and 56.