linear motion - kinematics
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Current Event Choose an article that is at least 2 pages in length if it is
in a magazine or at least 1 column if it is in a newspaper.If it is on the internet it should be a 5-8 paragraphs.
Read the article and write a summary of what the main
points of the article included.
On Friday we will discuss the articles. You should beworking from your summary during the discussion,
though you can bring the article in if you want to.
You will turn the summary in at the end of the period.
No late summaries will be accepted.
This article should concern either physics, weather,
astronomy or geology. NO BIOLOGY OR MEDICINE!
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Linear Motion - Kinematics
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Key Terms
Speed
Velocity
Acceleration Free fall
Gravity
Distance Displacement
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Linear Motion
Motion in a straight line
This motion can be described several ways: Speed
Velocity Acceleration
Distance
Direction
How can you tell when an object is moving? All motion is relative
Things that appear to be at rest can move
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Motion is Relative
Must compare two objects relative to oneanother. Called a frame of reference
How can you tell when an object is moving?
All motion is relative
Things that appear to be at rest can move Example:
You are sitting in class in your chair are youmoving?
Although you may be at rest relative to Earthssurface, youre moving about 100,000 km/hrelative to the sun.
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SpeedSpeed is one way to describe motion. It describes how
fast an object is moving using distance and time.
Average speed is the total distance traveled over the
total time and instantaneous speed is the speed at a
particular moment
For example, 30 milesperhour means object travels
distance of 30 miles in an elapsed time of one hour. Writeas,
(SPEED) =(Distance traveled)
(Time elapsed)
30 miles per hour = 30miles
hour
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Practice:
What is the average speed of a cheetah that
sprints 100 meters in 4 seconds? How about if
it sprints 50 meters in 2 seconds?
A car has an average speed of 100 kilometers
per hour. How far does it travel in 30 minutes?
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Demo: Ball Races
Which ball wins the race, A or B?
A
BFinish
Line
Which ball has the larger average speed?
Which has the larger instantaneous speed at each point.
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Velocity
a description of how fast and in what direction
a vector quantity
Constant velocity is constant speed andconstant direction (straight-line path with no
acceleration).
Constant speed is steady speed, neitherspeeding up nor slowing down.
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Different types of velocity and speed
Average velocity/speed
A value summarizing the
average of the entire trip.
All thats needed is totaldisplacement/distance and
total time.
Instantaneous velocity
A value that summarizes thevelocity or speed ofsomething at a given instant
in time. What the speedometer in
you car reads.
Can change from momentto moment.
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When we say that an object is moving at
constant velocity we mean that it is
1) at rest,2) moving at an unchanging speed,
3) moving at an unchanging speed in a straight-
line path,
and that its acceleration is
4) zero.5) constantly increasing (or decreasing).
6) uniform.
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Practice
The speedometer of a car moving eastreads 100 km/h. It passes another carmoving west at 100 km/h. Do they have
same speed? Velocity?
During a certain period of time, the
speedometer of a car reads a constant 60km/h. Does this indicate a constantspeed? Constant velocity?
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Practice Problem
A car going 15m/s accelerates at 5m/s2 for
3.8s. How fast is it going at the end of the
acceleration?
First step is identifying the variables in the
equation and listing them.
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Practice Problem
A car going 15m/s accelerates at 5m/s2for
3.8s. How fast is it going at the end of the
acceleration?t=3.8s
vi=15m/s
a=5m/s2
vf=?
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Hidden Variables
Objects falling through space can be
assumed to accelerate at a rate of
9.8m/s2
. Starting from rest corresponds to a vi=0
A change in direction indicates that at some
point v=0. Dropped objects have no initial velocity.
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Practice Problem 2
A penguin slides down a glacier starting from
rest, and accelerates at a rate of 7.6m/s2. If it
reaches the bottom of the hill going 15m/s,
how long does it take to get to the bottom?
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AccelerationDefine accelerationas how fast velocity changes
Acceleration is a rate of a rate (units will have 2 timevalues)
(ACCELERATION) =(Change in Velocity)
(Time interval)
Note: An object accelerates anytime its velocity
changes.
Examples include:Object speeds up.
Object slows down
Object changes direction (curved path)
Best example of acceleration is objects in free fall
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Acceleration
Free-fall
falling under the influence of gravityonlywith no air resistance
freely falling objects on Earth gainspeed at the rate of 10 m/s eachsecond (more precisely, 9.8 m/s2)
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Gravity
Gravity causes an acceleration.
All objects have the same acceleration due togravity.
Differences in falling speed/acceleration aredue to air resistance, not differences in gravity.
g=-9.8m/s2
When analyzing a falling object, consider final
velocity before the object hits the grounds.
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Acceleration
Galileo first formulated the
concept of acceleration in his
experiments with inclined
planes.
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When we say that an object is being accelerated, we
mean that
1) it is at rest, 2) it is moving,
3) it is either at a state of rest or a state of constant
velocity,
4) its state of motion is changing,
and we define acceleration to be
5) a change in speed.
6) a change in velocity.
7) the rate at which speed changes.
8) the rate at which velocity changes.
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An object is accelerating if it moves
1) with constant velocity 2) in a circular path
3) in a straight-line path
because it is undergoing a change in its
4) speed.
5) direction
6) net force.
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A car increases its speed from 60 to 65 miles per
hour in the same time that a bicycle increases its
speed from rest to 5 miles per hour. In this case the
acceleration is greater for the
1) car,
2) bicycle,
3) is the same for each,
principally because
4) the car undergoes the greater change in velocity. 5) the bicycle has considerably less mass.
6) both undergo equal increases in speed during
the same interval of time.
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Equation for displacement
t
dv
fi vvv
2
1
tvd
tvvd fi 21
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Practice Problems
A car slows from 45 m/s to 30m/s over 6.2s.
How far does it travel in that time?
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A cyclist speeds up from his 8.45m/s
pace. As he accelerates, he goes 325m
in 30s. What is his final velocity?
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Equation that doesnt require vf
tvvd fi 21 atvv if
tatvvd ii 21
)2(2
1 atvtd i
2
21 attvd i
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Practice Problems
A ball rolling up a hill accelerates at5.6m/s2
for 6.3s. If it is rolling at 50m/s initially, how far
has it rolled?
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If a car decelerates at a rate of4.64m/s2
and it travels 162m in 3s, how fast was it
going initially?
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An equation not needing t
tvvd fi 21atvv if
atvv if
ta
vv if
a
vvvvd
if
fi21
a
vvd
if
22
21
222 if vvad
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A bowling ball is thrown at a speed of
6.8m/s. By the time it hits the pins 63m
away, it is going 5.2m/s. What is theacceleration?
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The Big 4
atvv if advv if 222
tvatdi
2
2
1
tvvd
fi
2
1
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A plane slows on a runway from 207km/hr
to 35km/hr in about 527m.
a. What is its acceleration?
b. How long does it take?
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Ticker Tapes
A common way of analyzing the motion of objects in physics labs is toperform a ticker tape analysis. A long tape is attached to a movingobject and threaded through a device that places a tick upon the tapeat regular intervals of time say every 0.1 second. As the objectmoves, it drags the tape through the "ticker," thus leaving a trail ofdots. The trail of dots provides a history of the object's motion and istherefore a representation of the object's motion.
The distance between dots on a ticker tape represents the object'sposition change during that time interval. A large distance betweendots indicates that the object was moving fast during that timeinterval. A small distance between dots means the object was movingslow during that time interval. Ticker tapes for a fast-moving and aslow-moving object are depicted below.
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The analysis of a ticker tape diagram will also reveal if theobject is moving with a constant velocity or with a changingvelocity (accelerating). A changing distance between dotsindicates a changing velocity and thus an acceleration. A
constant distance between dots represents a constant velocityand therefore no acceleration. Ticker tapes for objects movingwith a constant velocity and an accelerated motion are shownbelow.
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Uniform Motion
Position vs. Time Graph Velocity vs. Time Graph
Nonuniform Motion - Changing Velocity
Position vs. Time Graph Velocity vs. Time Graph
Q: What does the slope
on a Position vs. Time
Graph tell us?
Q: What does the slope on a
Velocity vs. Time Graph tell
us?
A: The slope on a Position vs. TimeGraph tells us the velocity. A positive
slope indicates a positive velocity. A
negative slope indicates a negative
velocity.
A: The slope of a velocity vs. time graphtells us the acceleration. A positive
slope indicates a positive acceleration. A
negative slope indicates a negative
acceleration.
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The slope or gradientof a distance-time graph isincreases with speed.
distance
time
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Question 2Describe the motion of the three buses X, Y and Z
shown in the graph below.
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Uniformly Accelerating Objects
You see the car move
faster and faster. This is a
form of acceleration.
The position vs time graph
for the accelerating carreflects the bigger and
bigger Dx values.
The velocity vs time graph
reflects the increasingvelocity.
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Velocity-time graphs
velocity
time
The slope of a
velocity-time graph
represents
acceleration.
constant velocity
or zero acceleration
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Constant Velocity
This graph shows that
the velocity:1. is 1 m/s.
2. stays constant at 1 m/s
for 10 seconds.
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Activity #1 Predicting the fall time of
a ball
Predict how long it will take for a ball to fall_____ meters
Show all your work and calculations
Test your hypothesis and actually time the fall Perform at least 8 trials and find the average
fall time
Plug your time and distance values into anequation to find the acceleration (a or g) andsee how close your value comes to 9.8 m/s/s
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Activity #2
Reaction Time
Use a ruler/meter stick and calculate
your reaction time
Compare this to class/larger sampling size averages
Have one partner hold a ruler/meter stick vertically. The otherpartner places their hand at the 0 cm mark. Catch the ruler andrecord the distance.
Record the drop distance in cm 5 times and find the average
Calculate your average reaction time using the distance formula,
being careful to make sure your units are converted! The average reaction time for the general population is
approximately 0.2 0.25 seconds
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Activity #3 Tin pan alley Galileo conducted an experiment similar to this to help him
determine the equation for free fall in relation to distance, timeand gravity.
Attach a set of 6 inch hex nuts to a string so that the nuts will
hit the pie pan at equal time intervals
Place your first hex nut at 15 cm The falling nuts will accelerate (speed up) as they fall due to
gravity. How will you have to place your hex nuts on the string
so that the clangs occur at equal time intervals?
Are there any equations that can help you calculate the proper
distances?
Record the exact spacing between the nuts that resulted in the
clangs occurring at equal time intervals. Show all calculations!!
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