Chapter 2- Motion in 1 dimension Types of motion Translation - moving along a path (straight or curved) Rotation - rotating head over feet

Chapter 2- Motion in 1 dimension

Types of motion

Translation- moving along a path (straight or curved)

Rotation -rotating head over feet

How can you tell if something is in motion?

It is changing position

How can you tell if something is changing position

Is my desk moving?

Note solar system not to scale

Our approximate location in the Milky Way Galaxy

Our “local group” of galaxies

The motion of an object must be judged relative to a reference point.

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Compared to the sign the car is moving

By need, we unconsciously judge the motion of an object as COMPARED to something else.

example: You have your foot on the brake but the car next to rolls back

If you were in a spaceship with nothing in site, could you devise an experiment to determine if you were in motion (at a constant speed) or if you were stationary?

NO, but you could determine if you were changing speed or direction (accelerating)

The first postulate of Einstein’s Special Theory of relativity,is that there is no stationary reference point in the universe by which to to judge the motion of other object.

A reference point must be chosen, and the choice is arbitrary.

One frame of reference is not better than another with the exception of convenience.

Relative Motion Applet

What would be different if you were stationary and everything was moving toward you?

Frame of reference- Its all relative

When describing motion, you must choose an object or point to judge by

A

B C

Train is moving 50 m/s

D3 m/s 5 m/s

What is the relative speed betweenA & B A & DB & C B & DA & C C & D

50 m/s3 m/s53 m/s

45 m/s5 m/s8 m/s

There are many different ways to represent motionWords

PicturesEquations

Graphs

Describing motion

How could you describe the motion of an object?

SPEED

Describing motion


Direction

Describing motion


Speeding up, slowing down, constant speed

Describing motion


Straight Line PathTurning

We will look translation in 1 dimension 1st

y

x

Displacement:The straight line distance and

direction from the starting position to the final position.

When dealing with motion on the x-axis (horizontal) the following notation is used

0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

xStart Finish

x1 x2

x = x2 - x1

Displacement =

Other common notation used

0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

xStart Finish

xi xf

x = xf - xi

Displacement =

Other common notation used

0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

xStart Finish

xo x

x = x – x0

Displacement =

The FINAL POSITION (in the x axis) is referred to as

0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

xStart Finish

xo = 0 m x = 40 m

0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

xStart Finish

x = x2 - x1

Displacement =

Will the displacement be + or – 40 m?

ORDER COUNTS!! -40 m

0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

xStart Finish

The sign on the number indicates DIRECTION

ORDER COUNTS!!

x = + 40 mA 40 m change in the positive x direction!!

0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

xStartFinish

What is the displacement?

ORDER COUNTS!!

x = 50 m – 80 m = - 30 m

Often the standard Cartesian coordinate system is used.

+y

+x-x

-y

But you can choose to flip them for convenience, if you are consistent.

+y

+x -x

-y

But you can choose to flip them for convenience, if you are consistent.

I’ll show you what I mean.

You can even move around the origin.

0 m 10 m 20 m 30 m 40 m 50 m 60 m

Start Finish

-10 m-20 m-30 m-40 m

x = 30 m – 0 m = + 30 m

Where is the origin, and what is the positive x direction?

+ x

0 m 10 m 20 m 30 m 40 m 50 m 60 m

Start Finish

-10 m-20 m-30 m-40 m

x = 30 m – 0 m = + 30 m

0 m10 m20 m30 m40 m50 m60 m

Start Finish

Where is the origin, and what is the positive x direction?

+ x

+ x

70 m80 m90 m -10 m

x = 20 m – 50 m = - 30 m

If you get to pick (instead of me or the book)

Usually you will pick the starting point as “0”&

The positive direction as the direction of motion

x

0 m 10 m-10 m

start

Increasing X

Changing the coordinate system

-50 m -40 m -30 m -20 m -10 m 0 m 10 m 20 m 30 m 40 m 50 m

x

StartFinish

Displacement = -20 m - 0 m = -20 m

Changing the coordinate system

100 m 90 m 80 m 70 m 60 m 50 m 40 m 30 m 20 m 10 m 0 m

x

StartFinish

Displacement = 70 m - 30 m = 40 m

In this system, a positive vector indicates moving to the left

In this system is a positive displacement moving left or right?

-100 m -90 m -80 m -70 m -60 m -50 m -40 m -30 m -20 m -10 m -0 m

x

Displacement = -30 m - (-50 m) = 20 m

Start Finish

In this system, a positive vector indicates moving to the Right(the numbers get bigger to the right)

-50

m-4

0 m

-30

m-2

0 m

-10

m0

m10

m20

m30

m40

m50

m

Start

Finish

Displacement =

-10 m – (-30) m = +20 m

y = y2 – y1

Moving in the Y axis

Displacement and Distance have different meanings.

Distance: the total path length traveled

Displacement:The distance and direction from the

starting position to the final position.

Distance vs Displacement

Distance - the total distance traveled

Displacement - the distance between the starting and ending point

start

Finish

You leave your home to shop and upon your return, your odometer reads 5.2 miles more than when you left.

Sprawl-Mart

What is the distance and displacement for your trip?

A dragon flies in a straight line for 5 km. What is the distance and displacement?

Both 5 km

Find the distance and displacement

0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

x

StartFinish

Displacement = 30 m - 60 m = - 30 m

The negative sign indicates movement to the left on this system


0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

x

Start Finish

Displacement = 60 m - 20 m = +40 m

displacement

Is distance the same?

Distance = 80 m + 40 m = 120 m


0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

x

StartFinish

Displacement = 50 m - 90 m = -40 m

displacement

Is distance the same?

Distance = 80 m + 40 m = 120 m

Looking for direction?

VECTORS

Scalar- just indicates magnitude

Measurements or calculations come in two basic flavors

Vectors- indicates magnitude and direction

30 cm 55 mph 65 kg

35 knots S-SW 35 mph West 65 km North

Which would not make sense as a vector?(having a direction associated with it)

Displacement

Mass

Temperature

Velocity

Time

Force

Vectors can be represented using textor straight arrow.

X = +5.0 m

5.0 m East

5.0 m

They all give you the same info!

Why use an arrow instead of a straight line?

5.0 m

5.0 m

VectorsThe length indicates the magnitude

Scale: 1 cm = 5 m

The vectors have the same direction but different

magnitudes

VectorsThe arrowhead tells the direction

Scale: 1 cm = 5 m

The vectors have the same magnitude but different

directions

If you want to show that a variable is a vector you can

F

F

Have an arrow above it

be in bold

(I usually don’t do this on the board, because it is understood that certain things are vectors)

or

Distance Displacement

startFinish

Which could be represented by a vector?

Does the line indicate distance or displacement?

distance

displacement

If you wanted to determine the speed of a runner on a road,what equipment would you need? ( a radar gun is not allowed)

Speed = distance

time

Average Velocity

vavg =displacement

time

velocity is similar to speed but ….

Don’t need to write this down

Uses displacementIs a vector Uses distance

Is a scalar

Average Velocity

v =xt

vavg =displacement

time

Common shorthand for average is to put a line over it. v is pronounced “v bar”

v =xt

v =x2-x1

t2-t1

Mental Note:

This is shorthand….

for this.

velocity =displacement

time

Speed =distance

time

(speed & distance do not indicate direction)

A runner travels around a 400.0 m track in 40.0 seconds. What is their average speed & average velocity?

s = 10.0 m/s

v = 0 m/s

Velocity will have the same direction as displacement

Will the velocity be positive or negative?

0 m 10 m 20 m 30 m 40 m 50 m 60 m 70 m 80 m 90 m 100 m

x

Start

Positive



-50 m -40 m -30 m -20 m -10 m 0 m 10 m 20 m 30 m 40 m 50 m

x

Start

What is the velocity if the displacement occurred over 10.2 s



-50 m -40 m -30 m -20 m -10 m 0 m 10 m 20 m 30 m 40 m 50 m

x

What is the average velocity if the distance was traveled in 40 s?

-100 m -90 m -80 m -70 m -60 m -50 m -40 m -30 m -20 m -10 m -0 m

x


Positive

What is the displacement of a car which drives with an average velocity of 23 m/s east for 15 seconds?

Why was this likely only the average velocity?

A boat travels at +15 km/hr for 30 km and then at +20 km/hr for another 80 km. What was the average velocity for the entire trip?

Using relative speed / velocity

Two cars are 100 km away from each other.What is their relative speed?

35 km/hr 65 km/hr

100 km

relative distance

Two cars are 100 km away from each other.When do they crash

35 km/hr 65 km/hr

100 km

After 1 hour

35 km 65 km

The same as if one car was still and the other had the relative speed

0 km/hr 100 km/hr

100 km

If two cars are pointed at each other.

Car one is traveling at 12.3 m/s E and car two is traveling at 24 m/s W.If they are initially 895 m apart. How long will it take for them to crash.What is each car’s displacement (don’t forget direction).

Two cars are 100 km away from each other.What is the relative speed between them

30 km/hr80 km/hr

100 km

Two cars are 100 km away from each other.When do they crash?

30 km/hr80 km/hr

100 km

0 100 200 300

0 100 200 300

80

0 100 200 300

130

1 Hour

0 100 200 300

160

2 Hours

You have a collection of marbles, ranging from small (100 g) to big (500 g).

If the average mass is 300 g, how many marble in the collection will have a mass of 300 g?

100 500

500

100

100 500

500

100

300300 300300 300300

300300 300300 300300

300300 300300 300300

An average leaves a lot of information out!!

0.0 m 10.0 m

You race a friend to the wall in 2.0 seconds.What was your average velocity?

5.0 m/s E

East

0.0 m 10.0 m

You race a friend to a wall in 2.0 seconds.Your average velocity is

5.0 m/s E

East

v =

Why is this only an average?

Why is it just average?

A student hops in their car and drives east on the interstate. (We will call East the positive x direction)They arrive 51 miles away 1.5 hours later? The minimum speed limit is 40 miles an hour. Did they get a ticket for going too slow?

0 miles 51 miles

Time - 0 hr Time - 1.5 hr

v = 34 mihr

0 miles 51 miles

Time - 0 hr Time - 1.5 hr

mihr

No, they just stopped for lunch along the way

is just the average. They could have been driving 90 mph before and after lunch.

34

Average velocity = x t

Instantaneous velocity:your speed at a given moment in time

What does a speedometer tell you?

Average Speedor

Instantaneous Speed

A car finishes a 400.0 m run in 4.85 seconds.

Can you find the average velocity or the instantaneous velocity?

Is this average or instantaneous?

Read 2-2 & 2-3

Do WS 2.1

Using Pictures and Graphs to describe more than the average velocity.

(what goes on between the and finish)

??

Motion Graphs are a way of showing what happens between the start and finish. It is like the wall at the magic house (sort of).Pictures are taken at a CONSTANT TIME INTERVAL

What is the average velocity of the runner between “frames” if the time interval is 0.5 seconds?

0 m 1 m 2 m 3 m 4 m

What is the average velocity of the runner for the entire 4 m run? (taking 2 seconds)

0 m 1 m 2 m 3 m 4 m

What happens to the instantaneous velocity of the runner during the run?

0 m 1 m 2 m 3 m 4 m

0 m 1 m 2 m 3 m 4 m

If an object moves at a constant velocity, then the average velocity is also the instantaneous velocity at any point

If the time interval is the same what is different between the two velocities?

0 m 1 m 2 m 3 m 4 m

One travels a greater distance in the same amount of time.

0 m 1 m 2 m 3 m 4 m

What is happening to the speed?



Instead of Pictures we can also use….

What does this one tell you???

20 30 40100 m 50

A motion “graph” of a car.

What would it look like if it were actually graphed?

Time Vs Displacement Graph for a constant velocity

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20 30 40100 m 50


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If the velocity is CONSTANT, then the graph is a straight line. Why?


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What is the average velocity of the car over 100 seconds? Does it change?

v = xt

displacement -not change in x on the graph (sorry about the confusion)


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v = xt

What is the displacement after 100 s?

= 60 s – 0 s


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v = xt

What is the change in time for this?

= 0.6 m/s60 m – 0 m100 s – 0 s=


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v = xt = 0.6 m/s60 m – 0 m

100 s – 0 s=

Rise

Run

MAKE THE CONNECTION!!!!!!!

The slope of a displacement vs. time graph is the velocity of the object

Time Vs Displacement Graph

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What would be different if the object was moving twice as fast.


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Who is moving faster Blue or Green

Green– The bigger the slope, the bigger the velocity!!

4 m10 s

=0.4 m/s

13 m10 s

= 1.3 m/s


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What is the velocity (slope) indicated?


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What is the velocity (slope) indicated?


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What is the velocity?What is the object doing?


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The graph represents 2 cars on a track.What does it mean & what does the intersection of the 2 lines represent?


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Interpret the graph


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Interpret the graph


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What happened here?


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What happened here?


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Which object is moving faster?


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Interpret the graph

What happens to the slope of the curve?

Compare the distance traveled in the first 10 seconds vs. the last 10 seconds.


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What type of motion does this graph depict? & what direction

4.8 m/s

0.6 m/s0.1 m/s

Slowing DOWN Positive Velocity


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4.8 m/s

0.6 m/s0.1 m/s

Are these velocities Average or Instantaneous

Average over the time (run) in the slope


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4.8 m/s

This is still the average velocity over the 10 seconds, because the velocity changes over the 10 seconds. How do we know the velocity changes?

The line CURVES


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To find the instantaneous velocity at say 10 seconds. We would need to know the slope at THAT POINT.

We could shrink our time frame used until it is only at that point


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The INSTANTANEOUS Velocity at a time, is the SLOPE of a TANGENT LINE at that point.


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Notice what happens to the slope of the tangent lines…

Applet: sports car showing instantaneous velocity as the slope of the tangent line. (bottom of page)

Note no link??


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Find the instantaneous velocity of the car at 30 seconds.


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Car “A”

Car “B”

Describe the scenario

Car “A” starts out in front of “B” and moves at a constant speed

Car “B” accelerates and overtakes “A”


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Car “A”

Car “B”

Describe the scenario

Car “A” starts out in front of “B” and moves at a constant speed

Car “B” accelerates and then decelerates to runs along side “A”

Car “A”

Car “B”


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Car “A”

Car “B”

Car “A”

Car “B”

Where is car “B” moving the fastest?

Read section 2-4

Do WS 2.2

Now what is Acceleration

If you accelerate, you change your velocity. How could you change your velocity?

Speeding up

Slowing down

Changing Direction

Is acceleration a vector?

Going from 25 mph to 55 mph?

Going from 55 mph to 0 mph?

Changing direction to the east at a constant speed

IS THIS ACCELERATION?

Average acceleration

a =

vt

v2-v1

t2-t1

a =

Acceleration is rate at which you change velocity!!!

vta =

What are possible units of acceleration

s

ms

1s1s

xms2=

If an object initially at rest experiences a constant acceleration of +6 m/s2.

Time (s)

0123

Velocity (m/s)

0

61218

If an object initially moving at 10 m/s experiences a constant acceleration of 4 m/s2.

Time (s)

0123

Velocity (m/s)

10

141822

Two race cars start from a dead stop.

Car 1

Reaches a speed of 51 m/s in 5.6 s

Car 2


Which car had the greater acceleration?

In another race, two race cars start from a dead stop.

Car 1


Car 2


Which car had the greater acceleration?

The Porshe Boxster can reach 97 km/h from rest in 4.6 seconds. What is its average acceleration.

A car is moving at 58 m/s when it opens its chute and comes to a stop 38 seconds later. What is the acceleration during this time?

a = v2-v1

t2-t1

-

-=

ms0 m

s58

38 s 0 s= -1.5 m

s2

Why negative???

An object acceleratesspeeds upslows downchanges direction

DUE TO A FORCE.

An object will accelerate in the same direction as that of the applied force!

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velocity

The velocity is positive

Positive acceleration will cause The car to speed up

Negative acceleration will cause The car to slow down

Positive acceleration

Negative acceleration

01

23 m

The velocity is negative

Positive acceleration will cause

The car to speed upNegative acceleration will cause

The car to slow down

velocity


Negative acceleration

x

01

23 m


x

0

1

2

3 m


Two cars are initially stopped, the show positive acceleration. Which way to they move?

If an object initially moving at +10 m/s experiences a constant acceleration of -5 m/s2.

Time (s)

0123

Velocity (m/s)

10

50-5

What will happen to an object with a positive velocity, if it continues to negatively accelerate.

It will slow down, then…

It will STOP, then…

Go backwards, then…

A car initially is moving at 5.6 m/s. It accelerates at a rate of -1.1 m/s2 for 6.0 seconds. What is its final velocity?

A car travels a constant 35 m/s for 7.0 seconds. What is its acceleration?

Displacement vs Time graph review ( with signs)


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What is the sign (+ -) for the depicted:Velocity?

Acceleration?


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What does the Y- Intercept mean here???


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What type of motion does this graph depict? & what direction

Forward, Slowing DOWN Positive VelocityWhich means the acceleration is… negative


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What is the sign (+ -) for the depicted:Velocity?

Acceleration?


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What type of motion does this graph depict? & what direction?

Speeding up Negative velocity

Which means the acceleration is… negative


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What type of motion does this graph depict?

Speeding up positive velocity

Which means the acceleration is… positive


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Constant positive velocity

stopped

Which means the acceleration is…

But the overall acceleration is negative

Zero acceleration here


0

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0 10 20 30 40 50 60 70 80 90 100 110Time (s)

Dis

pla

ce

me

nt(

m)


Constant negative velocity

Constant positive velocity

What about the overall acceleration?


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nt(

m)


Slowing positive velocity

stopped

Speeding up negative velocity

Applets for graphs 2.1,2.2Exploration 2.1, 2.2Problems 2.1

Read 2-5Do problems page 43#’s 13,14 13 is 4.3 m/s2

14 is 5.2 s

Note for next year do 1st 3 problems on 2.3

Documents

Chapter 2- Motion in 1 dimension Types of motion Translation - moving along a path (straight or curved) Rotation - rotating head over feet