Chapter 2: Linear Motion

Mr. Miller

Conceptual

Physics

• Motion is relative

• An object’s motion is always

described in reference to another

object

Relative Motion

• When an object is said to be

traveling at 60 km/h, it is implied

that it is moving at 60 km/h

relative to the Earth.

Relative Motion

Jamiroquai

“Virtual Insanity”

Travelling Without Moving

1997 Video of the Year

Relative Motion

Relative Motion: Virtual Insanity

Vector- a quantity possessing both

magnitude and direction

Scalar- a quantity possessing only

magnitude

Vectors and Scalars

Examples of Vectors:

• Displacement (Δx)

• Velocity (v)

• Acceleration (a)

• Force (F)

• Momentum (p)

Vectors and Scalars

Examples of Scalars:

• Distance (d)

• Mass (m)

• Speed (v)

• Time (t)

Vectors and Scalars

Instantaneous speed: the speed

that something has at any one

instance

Average speed: the speed of an

object over a time interval

Speed

Speed

The average speed for a trip might

be 53 miles/hour.

...or 70 miles/hour on the open road.

However, during this trip your

instantaneous speed might have

been 0 miles/hour at a stoplight...

Speed

What are the units of speed?

• miles/hour…………….mph

• kilometer/hour……….km/h

• meters/second……….m/s

• furlongs/fortnight?

Speed

1. What is the average speed of a cheetah

that sprints 100 meters in 4 seconds?

2. How about if it sprints 50 m in 2 s?

Velocity

Velocity = {speed with a direction}

Examples:

70 mph is a speed.

70 mph North is a velocity.

Velocity

What are the units of velocity?

Velocity has the same units as

speed except they also have a

direction

Velocity and speed equations

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Velocity vs. speed

The speedometer of a car moving to the

east reads 100km/h. It passes another

car that moves to the west at 100km/h.

• Do both cars have the same speed?

• Do they have the same velocity?

• In an unusual move by the New York State

Department of Transportation, all of the "speed

limit" signs were replaced with "velocity limit"

signs.

– What would such a sign look like?

– How could one travel faster than the old speed limit

without violating the new velocity limit?

Conceptual Review

• Which device(s) on a car can

be used to change …

–its speed?

–its velocity but not its speed?

Conceptual Review

• A car driving on a circular test track shows a

constant speedometer reading of 100 kph for

one lap.

– Describe the car's speed during this time.

– Describe its velocity.

– How do the speed and velocity compare?

Conceptual Review

• Is it possible for an object to have …

–constant speed and changing

velocity,

–changing speed and constant

velocity?

Conceptual Review

• Why are the devices in cars

called speedometers and

not velocitometers?

Conceptual Review

OK Go

“Here It Goes Again”

Oh No

2007 Grammy award for "Best Short-Form Music Video”

Relative Motion…one more time

Relative Motion…one more time

Acceleration

Acceleration is the rate of change of velocity.

Acceleration

What are the units of acceleration?

• miles/hour/second…………….mi/h/s

• kilometer/hour/second……….km/h/s

• meters/second/second……….m/s/s or m/s2

Acceleration equations

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Acceleration

Acceleration is the positive or

negative depending on the

direction of the acceleration.

Acceleration

An object traveling with a constant positive velocity

Acceleration

An object traveling with a constant negative velocity

Acceleration

An object traveling with a positive velocity, positive acceleration.

Acceleration

An object traveling with a positive velocity, negative acceleration.

Acceleration

An object traveling with a negative velocity, negative acceleration.

Acceleration

An object traveling with a negative velocity, positive acceleration.

Free fall

Free fall is a state of falling free

from air resistance and other forces

except gravity.

Free fall

All free-falling objects

(on Earth) accelerate

downwards at a rate of

approximately 10 m/s2

(to be exact, 9.8 m/s2).

Free fall

Acceleration due to gravity = g

g = -9.8 m/s2

In some worksheets we will estimate g = -10 m/s2

In the absence of air

resistance, all objects

fall with the same

acceleration,

although this may be

hard to tell by testing

in an environment

where there is air

resistance.

Free fall

Coin and Feather Movie

Free fall

Feather and Hammer on the Moon Movie

Free fall

For objects dropped from rest

(v1 = 0 m/s)

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Time for a Gizmo!

Free fall

A ball is thrown up with an

initial velocity of 19.6 m/s.

What will the velocity and

displacement of the ball be after

1 second? 2 seconds? 3 seconds?

4 seconds ? Use -9.8 m/s2 for g.

Graphs of Motion

On a displacement vs. time graph the slope of

the line is equal to the velocity of the object.

On a velocity vs. time graph the slope of the line

is equal to the acceleration of the object.

On a velocity vs. time graph the area underneath

the curve is equal to the displacement of the object.

Graphs of Motion

An object traveling with a constant positive velocity

Graphs of Motion

An object traveling with a constant negative velocity

Graphs of Motion

An object traveling with a positive velocity, positive acceleration.

Graphs of Motion

An object traveling with a positive velocity, negative acceleration.

Graphs of Motion

An object traveling with a negative velocity, negative acceleration.

Graphs of Motion

An object traveling with a negative velocity, positive acceleration.

x vs. t graph v vs. t graph

Describe the motion.Object standing still at 20 m.

x vs. t graph v vs. t graph

Describe the motion.Object traveling at a constant 10 m/s

x vs. t graph v vs. t graph

Describe the motion.Object traveling at a constant -10 m/s

x vs. t graph v vs. t graph

Describe the motion.Object traveling at a constant 20 m/s for

2 seconds and then stands still at 40 m.

x vs. t graph v vs. t graph

Describe the motion.Object traveling at a constant 20 m/s for

2 sec and then a constant -20 m/s for 2 sec.

x vs. t graph v vs. t graph

Describe the motion.Object traveling at a constant negative velocity, stops for

a while, then travels at a positive velocity.

x vs. t graph v vs. t graph

Describe the motion.Object traveling at a constant

acceleration of 0.2 m/s2.

x vs. t graph v vs. t graph

Describe the motion.Object traveling at a constant

acceleration of -0.2 m/s2.

x vs. t graph v vs. t graph

Describe the motion.Object traveling at a constant acceleration of -0.2 m/s2.

Notice the velocity goes from being positive to negative.