Linear Motion - Kinematics

7/28/2019 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!!

Linear Motion - Kinematics

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