### Linear Motion

Linear Motion
Unit 1
Velocity and Acceleration
Objectives:
• Define the concept of average velocity in a way that shows you
know how to calculate it
• Calculate average velocity and to solve an equation involving
velocity, distance, and time
• Interpret and plot position-time graphs for positive and negative
velocities
• Determine the slope of a curve on a position-time graph/velocitytime graph and calculate the velocity or acceleration
• Distinguish instantaneous from average velocity
• Define average and instantaneous velocity
• Be able to calculate average velocity, given two velocities and the
time interval between them
• Be able to calculate final velocity in the case of uniform acceleration
• Be able to solve problems of motion of objects uniformly
accelerated by gravity
• Calculate distance fallen in an object affected by gravity
• Learn to use an organized strategy for solving motion problems
Speed
• Instantaneous speed-
– Example: Car speedometer
• Average speed-
Velocity
Instantaneous velocityv =
d
t
v = velocity, m/s
d = displacement, m
t = time, s
d
V
t
Average velocityCan you have a negative velocity? Why or why not?
 v = d
t
SI Units: m/s
 v = average velocity, m/s
d = displacement, m
t = time, s
English: miles/hour
Example 3.1
Suppose a 100 m walk takes 80 seconds. What is the
average velocity?
Example 3.2
In the Summer Olympics the 100-m race was won in 9.83s.
Find the average velocity in m/s.
Known
Unknown
Equation
Example 3.3 (pg. 43)
A. What is the average speed of a cheetah that sprints
100 meters in 4 seconds?
B. How about if the cheetah sprints 50 meters in 2
seconds?
Example 3.4 (pg. 43)
If a car moves with an average speed of 60 km/h for an
hour, it will have traveled a distance of 60 km.
A. How far would it travel if it moved at a rate for 4 h?
B. For 10 h?
Example 3.5 (pg. 43)
In addition to the speedometer on the dashboard of every
car is an odometer which records the distance traveled. If
the initial reading is set at zero at the beginning of a trip
and the reading is 40 km one-half hour later, what has been
Example 3.6 (pg 43)
Would it be possible to attend this average speed and never
go faster than 80km/h?
Position
Draw a Graph of "Speeding Up"
Time
Graphing Velocity
-
Position
Draw a Graph of "Slowing Down"
Time
Graphing Velocity
-
Position
Draw a Graph of “Constant Speed”
Time
Graphing Velocity
-
Comparisons
• http://www.exploratorium.edu/baseball/reactiontime.html reaction time activity
• reaction time of fox sports science episode 3 – Any (approx.
12 minutes)
• http://www.pbs.org/wgbh/nova/barrier/ - faster than sound
information
Acceleration
Average accelerationa = v
t
a=
v=
t=
SI units = m/s2
English: mi/h
instantaneous accelerationa= v
t
v
a
t
Example 3.7
Suppose you plan to attend the Pittsburgh Steelers home-opener.
The distance from Hollidaysburg to Pittsburgh is 90 miles (145 km).
a) If you are able to average 45 mph (20 m/s), how
long will it take you to travel to the game?
b) As you pull into the parking lot, you decrease your
speed from 20 m/s to 0 m/s over a time period of
4.0 seconds. What is your acceleration?
Example 3.8
A car accelerates along a straight road from rest to 28 m/s in 5.0
s. What is the magnitude of its average acceleration?
Known
Unknown
Equation
Example 3.9 (pg. 46)
What is the acceleration of a race car that whizzes past you at a
constant velocity of 400 km/h?
Example 3.10
The velocity of a car increases from 2.0 m/s at 1.0s to 16 m/s at
4.5 s. What is the car’s average acceleration?
Known
Unknown
Equation
Example 3.11
A car goes faster and faster backwards down a long driveway.
We define the forward velocity as positive, so backward velocity
is negative. The car’s velocity changes from –2.0 m/s to –9.0 m/s
in a 2.0s time interval. Find the acceleration.
Known
Unknown
Equation
What is going on in this graph?
What can you tell from this graph?
What can be read from this graph?
Explain the motion shown in the graph
Review!!!!
Aristotle (384 - 322 BC)
Earth-centric perspective
Proposed Two Types of Motion:
Natural Motion
Objects in the universe have a proper place
based on their nature.
ROCK SMOKE FEATHER - .
Heavier objects fall faster than light ones
Violent Motion
Resulted from pushing/pulling forces
Sustained motion required a sustained force
- Pushing and moving a heavy rock
- Bow and arrow
Copernicus (1543)
Sun is the center of the solar system
Galileo (1564-1642)
Provided evidence that Aristotle's views were
inaccurate.
Leaning Tower of Pisa Experiment
Inertia (Inclined Plane Experiments)
Galileo's Labs
Galileo's Inclined Plane Experiment
Physics
Unit 1 - Motion
Name: ______________________
Period: _____
Data Table
Angle of Incline (o)
Distance Traveled (cm)
Acceleration (m/s )
2
-
Acceleration due to gravity
How Fast- Free Fall
• Freefall- - occurs when gravity is the only force that
acts on an object
•
- No air resistance (in a perfect world)
Can take place when:
• - an object is falling
• - an object is rising
• - an object is traveling at an angle
• - an object is momentarily at rest at its
highest point
Freefall Continued
Gravity(g)- force of attraction between 2 masses
Terminal Velocity-constant maximum velocity
reached by a body falling under gravity
through a fluid
g = 10 m/s
g = v
t
2
Example 3.12 (pg. 48-49)
Using the speedometer on Figure 3.7 what would the
6s after it is dropped? 6.5 seconds?
Example 3.13
The time the Demon drop ride at Cedar Point, Ohio is free falling
is 1.5 s. What is the velocity at the end of this time?
Known
Unknown
Equation
Free Fall Lab
Object
Small blue square
Medium blue square
Large blue square
Softball
Acceleration(m/s2 )
How Far
d = 0.5 gt2
Example 3.14 (pg. 50)
A car steps off a ledge and drops to the ground in 0.5
seconds.
A. What is it’s speed on striking the ground?
B. What is its average speed during the 0.5 seconds?
C. How high is the ledge from the ground?
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http://www.fearofphysics.com/Xva/xva.html
http://www.fearofphysics.com/Fall/fall.html
http://www.fearofphysics.com/Roller/roller.html
http://video.msn.com/?mkt=en-us&brand=foxsports&vid=fce2cab5-a3004f78-880c-18be6d3e3fc2&from=Fox%20Sports&tab=g1196965174236 Ben Rothelsberger and getting off a pass- may not work, but google search
http://www2.swgc.mun.ca/physics/physlets/motiona.html - position vs.
time graphs
http://www2.swgc.mun.ca/physics/physlets/motionb.html - velocity vs.
time graphs
http://www2.swgc.mun.ca/physics/physlets/motionc.html - acceleration
graphs