usain bolt is the world’s fastest man!!!

Usain Bolt is the world’s fastest man!!!

Physics of Motion

• We will look at:– Position– Distance– Displacement– Speed– Velocity– Acceleration

• First you need to realize that motion is relative…

Motion is relative

• What is meant by saying that motion is relative? For everyday motion, what is motion usually relative to?

Motion is Relative

• Motion is relative to the observer’s position and their reference point– Sometimes called a “reference frame”

Consider the picture…

• If this man is driving at 15 mph, how fast is his coffee cup moving?

• Does the man feel like the cup is moving?

• Why?

Motion is relative

• An object is in motion if it changes position relative to a stationary reference point.

Use this to establish a COORDINATE SYSTEM• pick an origin or 0 point• decide which direction is positive

Direction

• We use N, S, E, W or left, right, up, & down to describe the direction of movement.

• We can also use POSITIVE and NEGATIVE to describe direction.

POSITION

A location with respect to the origin or zero point.

Finding Position

4 miles

6 miles

06-4

1040

0-6-10

Position depends on where you put ‘0’.

Distance and Displacement

• Distance measures the actual path an object takes

• Displacement measures your overall distance from the initial position to final position in a STRAIGHT LINE.

• DISPLACEMENT values must include a DIRECTION!

• Which color line represents distance?

• Displacement?

Speed vs Velocity: Scalars vs Vectors

All measured quantities can be classified as being either a

scalar or a vector.

Scalar

_________ only (size of the quantity ….a number)

Vector

_________ and _________

Magnitude

MagnitudeDirection

Distance vs. Displacement

• http://physics.info/displacement/

Write in your own words- what is the difference between distance and

displacement?

• Distance-

• Displacement-

Use the diagram to determine the resulting displacement and the distance traveled by the

skier during these three minutes. •

Answer

• The skier covers a distance of• (180 m + 140 m + 100 m) = 420 m and has a

displacement of 140 m, right or east.

Formula for DisplacementHow did you calculate displacement-

write a formula!

∆X = Xf-Xi

Xf= final positionXi= initial position

Remember- displacement can be positive or negative! (ex- what if you started at “B”?)

What is the coach's resulting displacement and distance of travel?

Answer

• The coach covers a distance of• (35 yds + 20 yds + 40 yds) = 95 yards and has a

displacement of 55 yards, left or -55 yards.

Speed

• Describes how fast an object moves.• We know some things move faster than

others…but how do we measure it?• What two quantities must you know to

determine speed?

What two quantities must you know to determine speed?

• Choose from: displacement, distance, time, velocity– Hint…what is speed measured in???

– Speed= distance/time• Ex- miles/hour, m/s, etc.

There are three types of speed you must know…

• Constant speed• Average speed• Instantaneous speed

Constant Speed

• When an object covers equal distances in equal amounts of time

• Ex- if a race car travels at a CONSTANT SPEED of 96m/s, it will travel a DISTANCE of 96 meters EVERY SECOND.

But most objects do not travel at a constant speed.

• The speed of an object can change from one minute to another.

• So we can use AVERAGE SPEED to describe its motion.

• Use this equation…

Average Speed = total Distance / total Time

Let’s try it• A runner finished a 3 mile race in 22 minutes.

He may not have run at the same pace the whole time, but you can still calculate his AVERAGE SPEED

• 3 miles/22 minutes=.14 miles/minPACE: • 22 minutes / 3 miles = 7.33 min/mile

Instantaneous vs. Average speed

• Average speed- overall distance over time the object traveled

• Instantaneous speed- measures speed over small time interval (at an instant)

• Does a speedometer of a car read instantaneous or average speed?

• What 2 controls on a car enable a change in speed?

What if I want to describe speed AND direction?

• For example…what if you wanted to find a plane. Knowing the speed would only tell you how far away to look but not in what direction. For that we need…

• VELOCITY- the speed and direction of motion.

Let’s get back to the car example…

• Name another control that enables a change in velocity.

So…What is the difference between speed and velocity?

• SPEED- reports the magnitude of distance over time (just the number).

• VELOCITY- reports the magnitude AND direction of motion.

So how do you calculate speed vs velocity?

• Speed = distance / time• Velocity = displacement / time

(Includes a direction!)

Are speed and velocity always going to be the same?

• NO! • Only if the object is moving in the SAME

direction the whole time.

• What is an example of a motion where avg speed is not equal to average velocity? (demo)

Let’s look closer…

• Average velocity is calculated by the equation:

Vavg= (xf-xi) / (tf-ti)

Use the diagram to determine the average speed and average velocity between the following points.

A. Going from A and BB. Going from A to B and ending at C•

Answers:

• A. Between A and B, speed and velocity will be the same because they are in the same direction the whole time. – Speed = 180 m/min– Velocity = 180 m/min east

• B. When the motion continues to point C, the speed and velocity are different because the distance traveled and displacement are different. – Speed= 320 m/2 min= 160 m/min– Velocity= 40 m/2 min= 20 m/min east

What is the coach's resulting displacement and distance of travel?

Let’s use our math skills

• Page 323…

• Read through “MATH SKILLS”• DO problems 1-3 “Practice Problems”

Answers to problems on 323

• 1. v=d/t110m/72 sec= 1.5 m/s toward shore

2. v=d/t38m/1.7 sec= 22m/s toward first base

3. d=vt=(12.0 km/hr)(5.00 hr)=60.0 or 6.00 x 104 m southwest

Acceleration

Chapter 10.2-3

• Actual definition is…any change in VELOCITY

Try to define the word

“acceleration”…

More specifically: Acceleration is a change in velocity in a period of time.

• So…Is it a vector or a scalar quantity?– VECTOR– It must include a direction (like velocity)

• This also means that you can change acceleration by changing what?– Speed or Direction

Does travel at a constant speed mean you are not accelerating?

• NO!!! • Remember that you can change velocity by

changing direction, thus CHANGING ACCELERATION!

When a ferris wheel goes up and around, what about its passengers is changing?

1. Speed2. Velocity3. Acceleration4. None of the above

So let me get this straight…

• Constant Speed means –– Something travels the same distance in each time interval

• Constant Velocity means- – Something travels the same distance, in the same direction in each

time interval

• So what about constant acceleration?

Constant Acceleration

• The velocity changes by the same amt over each time interval. (figure 11, p 329)

• Ex- centripetal acceleration– As the earth goes around the

sun, it travels at a constant speed– BUT since it is going in a circle,

it’s velocity is changing AT A CONSTANT RATE…therefore…

– CONSTANT ACCELERATION!

Causes of acceleration

• Increasing velocity– Example: Car speeds up at green light

• Decreasing velocity– Example: Car slows down at stop light

• Changing Direction– Example: Car takes turn (can be at constant

speed)

screeeeech

Question

• How can a car be accelerating if its speed is a constant 65 km/h?

• If it is changing directions it is accelerating

What do the numbers mean?

• Small acceleration – means speed is increasing slowly

• Large acceleration- means speed is increasing rapidly

Extension: • Acceleration can be positive or negative, but

negative acceleration doesn’t always mean the object is slowing down. – (it could also be changing direction)

Calculating AccelerationIf an object is moving in a straight line…• ∆V= change in velocity

(Final Velocity – Initial Velocity) (m/s)

• A= acceleration • ∆ T= time (s)

(final time- initial time)

So what are the units of acceleration? If A= V/T… Acceleration is in m/s2

A ∆T

∆V

Calculating Acceleration

0 s 1 s 2 s 3 s 4 s

0 m/s 4 m/s 8 m/s 12 m/s 16 m/s

2(16 / 0 / )4 /

4

m s m sm s

s

Acceleration = (Vf-Vi) t

Let’s look at the picture below…what is this car’s avg acceleration?

Question• A skydiver accelerates from 20 m/s to 40 m/s in 2

seconds. What is the skydiver’s average acceleration?

2/10

2

/20

2

/20/40

__

sm

s

sm

s

smsmTime

speedInitialspeedFinalAccel

2

( _ _ )

40 / 20 / 20 /( )10 /

2 2

Final velocity Initial velocityA

Timem s m s m s

m ss s

????

Constant velocity

Now consider a car moving with a rightward (+), changing velocity - that is, a

car that is moving rightward but speeding up or accelerating.

Acceleration

Distance time graphs

• Draw 2 graphs– One showing a slow constant speed– One showing a faster constant speed

Position-Time Graphs

Slow, Rightward(+)Constant Velocity

Fast, Rightward(+)Constant Velocity

More Position-Time Graphs

Slow, Leftward(-)Constant Velocity

Fast, Leftward(-)Constant Velocity

Consider a car moving with a constant, rightward (+) velocity - say of +10 m/s. A car moving with a constant velocity is a car with zero acceleration.

• Draw a graph!

Constant velocity = zero acceleration

Positive Acceleration

Now consider a car moving with a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating. Since the car is moving in

the positive direction and speeding up, the car is said to have a positive acceleration.

Positive acceleration

Describe this graph!

• Does the velocity of the wind affect such things as a sprinter’s speed or an airplane’s flight time?

Resultant Velocity animation

• http://www.glenbrook.k12.il.us/GBSSCI/PHYS/mmedia/vectors/plane.html

A small airplane heads east with a speed of 200 mph with respect to the air (the “air speed”). This would be the plane’s speed if the air was NOT moving – no wind)

• If the wind/jet stream is moving east at 50 mph, what is the plane’s resulting velocity with respect to the ground (the “ground speed”)?

“Adding Vectors” Example:

with the wind

200 50

250 mph, east

• If, later, the airplane is flying west into the 50 mph wind with an “air speed” of 200 mph, now what is the plane’s resulting velocity with respect to the ground (the “ground speed”)?

against the wind

50

200

150 mph, west

1. Find the velocity in m/s of a swimmer who swims 110 m toward the shore in 72 s.

• 1.5 m/s toward the shore

1. Imagine that you could ride a baseball that is hit high enough and far enough for a home run. Using the baseball as a reference frame, what does the Earth appear to do?

1. Calculate the displacement in meters a cyclist would travel in 5.00 h at an average velocity of 12.0 km/h to the southwest.

But first let’s look at some graphs…

• If I wanted to graph speed, what should I label my axes???

• So the slope of the line=SPEED

Dis

tance

Time

Speed

Constant Speed

• What would a position-time graph look like for a constant speed?