Types of Motion

PreAP Physics

YOU deserve a speeding ticket!Officer Friendly is the LAW around

here and the LAW says that the speed limit is 55 miles per hour!

Here is the scenario!

You wake up late and have 20 minutes to get to school and you especially do not want to be late for physics! You decide to travel at 65 mph in a 55 mph zone. Unfortunately, Officer Friendly pulls you over. You see, the LAW states that you must pay $10 for every mile you are over the speed limit. Therefore, you MUST pay $100 to cover the fine. Being a law abiding citizen you agree, and pay the fine. But as you begin to leave you hear Officer Friendly say……..

BUT WAIT!Our city council just recently passed a law 3 months ago that requires us to fine you for being on the planet Earth as it rotates on it’s axis. Since Earth rotates on its axis at 1000 mph you must pay ….

Motion Speed Over

Fine

On road 10 mph $100

Earth’s Rotation

1000 mph

But as you begin to leave you hear Officer Friendly say……..

$10,000

BUT WAIT!Our city council just last month passed a law that requires us to fine you for being on the planet Earth as it revolves around our Sun at a speed of 66,621 mph. Thus your fine is…..

Motion Speed Over

Fine

On road 10 mph $100

Earth’s Rotation

1000 mph $10,000

Earth’s Revolving

66,621 mph But as you

begin to leave you hear Officer Friendly say……..

$666,210

BUT WAIT!Our city council just last week passed a law that requires us to fine you for being on the planet Earth which moves towards Vega in the constellation Lyra at a speed of 44,041 mph. Thus your fine is…..

Motion Speed Over

Fine

On road 10 mph $100

Earth’s Rotation

1000 mph $10,000

Earth’s Revolving

66,621 mph

$666,210

To Vega 44,041 mph

But as you begin to leave you hear Officer Friendly say……..

$440,410

BUT WAIT!Our city council just yesterday passed a law that requires us to fine you for being on the planet Earth in the Milky Way which rotates at a speed of 558,900 mph. Thus your fine is…..

Motion Speed Over

Fine

On road 10 mph $100

Earth’s Rotation

1000 mph $10,000

Earth’s Revolving

66,621 mph

$666,210

To Vega 44,041 mph

$440,410

Milky Way 558,900 mph

Let me total your fine!

$5,589,000

You owe……(somehow)Your total fine is:

$6,705,720

Now be a law abiding citizen and PAY UP!

The bottom line….Motion is RELATIVEIt depends completely on how you want to look at the moving

object. You establish a frame of reference!

Example: You are sitting in an airplane which is moving at a speed of 100 km/h and there is a fly sitting on your head.

(a) What is your speed relative to the ground?

(b) What is your speed relative to the seat you're sitting it?

(c) What is the speed of the fly relative to you?

100 km/hr

0 km/hr

0 km/hr

DisplacementDisplacement (x or y)   "Change in position"

It is not necessarily the total distance traveled. In fact, displacement and distance are entirely different concepts. Displacement is relative to an axis.

o "x" displacement means you are moving horizontally either right or left.o "y" displacement means you are moving vertically either up or down.o The word change is expressed using the Greek letter DELTA ( Δ ).o To find the change you ALWAYS subtract your FINAL - INITIAL positiono It is therefore expressed as either   Δx = xf - xi or Δy = yf - yi

Distance - How far you travel regardless of direction.

ExampleSuppose a person moves in a straight line from the lockers( at a position  x =

1.0 m) toward the physics lab(at a position x = 9.0 m) , as shown below

The answer is positive so the person must have been traveling horizontally to the right.

ExampleSuppose the person turns around!

The answer is negative so the person must have been traveling horizontally to the left

What is the DISPLACEMENT for the entire trip?

What is the total DISTANCE for the entire trip?

mxxx initialfinal 00.10.1

m1688

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Average VelocityVelocity is defined as: “The RATE at which DISPLACEMENT changes”.

Rate = ANY quantity divided by TIME.

Average SPEED is simply the “RATE at which DISTANCE changes”.

t

ds

ExampleA quarterback throws a pass to a defender on the other team who

intercepts the football. Assume the defender had to run 50 m away from the quarterback to catch the ball, then 15 m towards the quarterback before he is tackled. The entire play took 8 seconds.

Let's look at the defender's average velocity:

smss

mm

t

xv /38.4

08

035

Let's look at the defender's speed:

sms

m

t

ds /125.8

8

65

“m/s” is the derived unit for both speed and velocity.

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Slope – A basic graph modelA basic model for understanding graphs in physics is SLOPE.

Using the model - Look at the formula for velocity.

Who gets to play the role of the slope?

Who gets to play the role of the y-axis or the rise?

Who get to play the role of the x-axis or the run? 

What does all the mean? It means that if your are given a Displacement vs. Time graph, to find the velocity of an object during specific time intervals simply find the slope.

t

xv

Run

Riseslope

Velocity

Displacement

Time

Displacement vs. Time graphWhat is the velocity of the object from 0 seconds to 3 seconds?

The velocity is the slope!

Displacement vs. Time graphWhat is the velocity of the object from 7 seconds to 8

seconds?  Once again...find the slope!

A velocity of 0 m/s. What does this mean? It is simple....the object has simply stopped moving for 1 second.

Displacement vs. Time graphWhat is the velocity from 8-10 seconds? You must remember! To

find the change it is final - initial.

The answer is negative! It is no surprise, because the slope is considered to be negative.

This value could mean several things: The object could be traveling WEST or SOUTH. The object is going backwards - this being the more likely choice!

You should also understand that the slope does NOT change from 0-3s , 5 to 7s and 8- 10s.

This means that the object has a CONSTANT VELOCITY or IT IS NOT ACCELERATING.

ExampleIt is very important that you are able to look at a graph and explain it's motion in great detail. These graphs can be very conceptual.

Look at the time interval t = 0 to t = 9 seconds. What does the slope do?

It increases, the velocity is increasingLook at the time interval t = 9 to t = 11 seconds. What does the slope do?

No slope. The velocity is ZERO.Look at the time interval t = 11 to t = 15 seconds. What does the slope do?

The slope is constant and positive. The object is moving forwards at a constant velocity.Look at the time interval t = 15 to t = 17 seconds. What does the slope do? The slope is constant and negative. The object is moving backwards at a constant velocity.

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E

D

C

A

B

position

time

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C

D

E

A

B

position

time

a) Which maintains constant velocity? b) Which accelerates? c) Which changes direction? d) Which is not moving? e) Which is the fastest constant velocity? f) Which is slowest constant velocity? g) Which has the greatest acceleration?

Acceleration PreAP Physics

The RATE of CHANGE of VELOCITY

Change = FINAL - INITIAL

v = Final velocity – Initial velocity

2///seconds

ondmeters/secsmorssm

t

va

Acceleration – The Definition

Example: A Cessna Aircraft goes from 0 m/s to 60 m/s in 13 seconds. Calculate the aircraft’s acceleration.

13

060

t

va 4.62 m/s/s

Example

Example: The Cessna now decides to land and goes from 60 m/s to 0 m/s in 11 s. Calculate the Cessna’s acceleration.

11

600

t

va - 5.45 m/s/s

Example

Notice: Initial velocity was positive (moving in the positive direction). The change in velocity is negative, so the acceleration is negative.

Sign Conventions

Remember: Positive or Negative refer to direction, not increasing or decreasing amount.

Speeding Up (velocity and acceleration have same sign)+v & +a -or- -v & -a

Slowing Down (velocity and acceleration have opposite signs)+v & -a -or- -v & +a

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If an object is in FREE FALL in the VERTICAL DIRECTION, the acceleration is due to GRAVITY.

ssmgay //8.9•It NEVER ceases to exist•It ALWAYS works DOWN

•It is NEVER zero•This is ONLY true in a vacuum (no air)

Free-Fall Acceleration

Example: A person throws a ball straight upward into the air.

Q1: What is the Acceleration at the TOP of its path? -9.8 m/s/s

Q2: What is the VELOCITY at the TOP of its path?ZERO

Acceleration due to Gravity

Q3: What is the magnitude(#value) and direction of the acceleration, HALF way up?

-9.8 m/s/s - ALWAYS DOWNWARD

Q4: What is the magnitude(#value) and direction of the acceleration, HALF way down?

-9.8 m/s/s - ALWAYS DOWNWARD

THE BOTTOM LINE: EVERYTHING will accelerate at -9.8 m/s/s in a VACUUM, that is any situation involving NO AIR.

Acceleration due to Gravity

Slopea

Runt

Risevt

va

Run

RiseSlope

Acceleration

What is the acceleration fromt=0s to t=3s?

60/3= 20 m/s/s

What is the acceleration fromt=3 s to t=5s?

0/2 = 0 m/s/s

What is the acceleration fromt=8s to t=9s?

0-60/1 = -60 m/s/s

Acceleration – Graphical Representation

Let’s Review

smslopeRun

Rise

t

xv /

seconds

meters

VELOCITY is the SLOPE of a distance, position, or displacementvs. time graph.

Let’s Review

What is the slope doing?

INCREASING

What is the velocity doing?

INCREASING

Let’s Review

ssmslopeRun

Rise

t

va //

seconds

ondmeters/sec

Let’s Review

Describe the accelerationduring interval A.

The acceleration or SLOPEis constant and positive.

Describe the accelerationduring interval B.

The acceleration or SLOPEis ZERO.

Describe the acceleration during interval C.

The acceleration or SLOPE is constant and negative.

Let’s Review

What is the acceleration(slope) doing?

The acceleration is INCREASING!

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A

B

C

D

E

tv

-

+

a) Which objects have constant velocity? b) Which objects are accelerating? c) Which objects are not moving? d) Which objects change direction? e) Which object has the smallest acceleration? f) Which object has the greatest velocity?

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Let’s Review

The slopes help us sketch the motion of other graphs!

NEW MODEL = AREA

seconds

meters x seconds meters

units of viewofpoint thefromit at Looking

AREAx

HEIGHTv

BASEt

HEIGHTxBASEAREAvtxt

xv

The Area ModelHow FAR did this object travel during intervalA?

mxorArea

AbhA

100

20102

1

2

1

How FAR did this object travel during intervalB?

mxorArea

AhbA

400

2020

How FAR did this object travel during interval

c?

mxorArea

AbhA

400

20402

1

2

1

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0 6t (sec)

v(m/s)

30

0 4t (sec)

v(m/s)

40

420 6t (sec)

v(m/s)

50

20

In summaryGraph Slope Area

x vs. t Velocity N/A

v vs. t Acceleration Displacement

a vs. t N/A Velocity

Slope Graph Area

x vs. t

v vs. t

a vs. t

t (s) t (s) t (s)

x (m)v (m/s) a (m/s/s)

slope

= v

slope

= a

area = xarea = v

Comparing and Sketching graphsOne of the more difficult applications of graphs in physics is when given a certain type of graph and asked to draw a different type of graph

t (s)

x (m)

slope

= v

t (s)

v (m/s)

List 2 adjectives to describe the SLOPE or VELOCITY1. 2.

The slope is CONSTANTThe slope is POSITIVE

How could you translate what the SLOPE is doing on the graph ABOVE to the Y axis on the graph to the right?

Example

t (s)

x (m)

t (s)

v (m/s)

1st line• •

2nd line•

3rd line• •

The slope is constant

The slope is constantThe slope is “+”

The slope is “-”The slope is “0”

Example – Graph Matching

t (s)

v (m/s)

t (s)

a (m/s/s)

t (s)

a (m/s/s)

t (s)

a (m/s/s)

What is the SLOPE(a) doing?

The slope is increasing

The Three Amigos! (aka Kinematic Equations)