PhysicsPhysicsPhysicsPhysics Unit 1 One-Dimensional Kinematics Reference Glencoe Chapter 2, Chapter 3.

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Unit 1Unit 1One-Dimensional KinematicsOne-Dimensional Kinematics

Reference Glencoe Chapter 2, Chapter 3Reference Glencoe Chapter 2, Chapter 3

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SP1SP1Students will analyze the Students will analyze the

relationship between force, mass, relationship between force, mass, gravity, and the motion of objects.gravity, and the motion of objects.

a. Calculate average velocity, a. Calculate average velocity, instantaneous velocity, and instantaneous velocity, and

acceleration in a given frame of acceleration in a given frame of reference.reference.

Mechanics – the study of how objects move Mechanics – the study of how objects move and respond to external forcesand respond to external forces

Kinematics – study of motion with no concern Kinematics – study of motion with no concern for the causefor the cause

One – Dimensional KinematicsCalculate average velocity, instantaneous velocity, and acceleration.

Coordinate System – define and origin and a Coordinate System – define and origin and a positive directionpositive directionMust remain consistentMust remain consistentIn one dimensionIn one dimension

1.1 Position, Distance, and DisplacementCalculate average velocity, instantaneous velocity, and acceleration.

Position – a reference to the coordinate Position – a reference to the coordinate systemsystem

Distance – total length of travelDistance – total length of travel

Displacement – (Displacement – (x) change in positionx) change in position

More commonly used in physicsMore commonly used in physics

Vector – magnitude and directionVector – magnitude and direction

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1.1 Position, Distance, and DisplacementCalculate average velocity, instantaneous velocity, and acceleration.

Displacement vs. distanceDisplacement vs. distance

1.1 Position, Distance, and DisplacementCalculate average velocity, instantaneous velocity, and acceleration.

Speed – distance per unit timeSpeed – distance per unit time

Average Velocity – (Average Velocity – (vv) displacement per unit ) displacement per unit timetime

t = change in time (t-tt = change in time (t-t00))

Velocity is a vector, so needs directionVelocity is a vector, so needs direction

In one dimension this is indicated by a + or - In one dimension this is indicated by a + or - signsign

t

xv

1.2 Average Speed and VelocityCalculate average velocity, instantaneous velocity, and acceleration.

Graphical Interpretation of Average VelocityGraphical Interpretation of Average Velocity

Slope of displacement time is average velocitySlope of displacement time is average velocity

Over any time period, slope between two Over any time period, slope between two points is average velocitypoints is average velocity

Displacement vs. Time

1.2 Average Speed and VelocityCalculate average velocity, instantaneous velocity, and acceleration.

smvs

mmv

t

xv

/83.06

16

1.2 Average Speed and VelocityCalculate average velocity, instantaneous velocity, and acceleration.

smvs

mmv

t

xv

/0.22

15

1.2 Average Speed and VelocityCalculate average velocity, instantaneous velocity, and acceleration.

Instantaneous velocity – average velocity over Instantaneous velocity – average velocity over very short period of timevery short period of time

Limited by math to situations with constant Limited by math to situations with constant accelerationacceleration

Slope of the tangent to the point on a graphSlope of the tangent to the point on a graph

t

xv

0t

lim

1.3 Instantaneous VelocityCalculate average velocity, instantaneous velocity, and acceleration.

smvs

mmv

t

xv

/96.18.2

05.5

1.3 Instantaneous VelocityCalculate average velocity, instantaneous velocity, and acceleration.

A man runs 3 m west in 2 seconds. What A man runs 3 m west in 2 seconds. What is his average velocity?is his average velocity?

He then runs south 4 m in 3 seconds. He then runs south 4 m in 3 seconds. What is his average speed from the What is his average speed from the time he started, and what is the time he started, and what is the magnitude of his average velocity?magnitude of his average velocity?

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Acceleration – (a) change in velocity per unit Acceleration – (a) change in velocity per unit timetime

Units are meters/secondUnits are meters/second22 (m/s (m/s22))

We will only deal with constant accelerationWe will only deal with constant acceleration

Deceleration – negative accelerationDeceleration – negative acceleration

Velocity and Acceleration same sign – object Velocity and Acceleration same sign – object speeds upspeeds up

Different sign – object slows downDifferent sign – object slows down

t

va

1.4 AccelerationCalculate average velocity, instantaneous velocity, and acceleration.

Slope of displacement graph is velocitySlope of displacement graph is velocity

Slope of velocity graph is accelerationSlope of velocity graph is acceleration

1.4 AccelerationCalculate average velocity, instantaneous velocity, and acceleration.

1.4 AccelerationCalculate average velocity, instantaneous velocity, and acceleration.

1.4 AccelerationCalculate average velocity, instantaneous velocity, and acceleration.

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SP1SP1Students will analyze the Students will analyze the

relationship between force, mass, relationship between force, mass, gravity, and the motion of objects.gravity, and the motion of objects.

b. Compare graphically and b. Compare graphically and algebraically the relationships algebraically the relationships

among position, velocity, among position, velocity, acceleration, and time.acceleration, and time.

Constant Acceleration – average acceleration Constant Acceleration – average acceleration = instantaneous acceleration= instantaneous acceleration

We will only study kinematics problems where We will only study kinematics problems where acceleration is a constantacceleration is a constant

The next slide lists the equations we will useThe next slide lists the equations we will use

Constant Acceleration

1.5 Motion with Constant AccelerationCompare the relationship among position, velocity, acceleration, and time.

xavv

attvxx

tvvxx

atvv

220

2

221

00

021

0

0

1.5 Motion with Constant AccelerationCompare the relationship among position, velocity, acceleration, and time.

Steps in problem solvingSteps in problem solving

1.1.Draw a diagramDraw a diagram

2.2.List known variablesList known variables

3.3.Stop and think through the physics that is Stop and think through the physics that is occurringoccurring

4.4.Think through steps and information Think through steps and information required to solve the problemrequired to solve the problem

5.5.Gather correct equations and solveGather correct equations and solve

1.5 Motion with Constant AccelerationCompare the relationship among position, velocity, acceleration, and time.

An airplane accelerates down a runway from An airplane accelerates down a runway from rest. The runway is 3000 m long and the rest. The runway is 3000 m long and the plane must have a speed of 65 m/s to take off. plane must have a speed of 65 m/s to take off. What is the minimum acceleration that will What is the minimum acceleration that will allow the plane to take off?allow the plane to take off?1.1.Draw a diagramDraw a diagram

2.2.List known variablesList known variables

3.3.Stop and think through the physics that is occurringStop and think through the physics that is occurring

4.4.Think through steps and information required to solve Think through steps and information required to solve the problemthe problem

5.5.Gather correct equations and solveGather correct equations and solve

1.5 Motion with Constant AccelerationCompare the relationship among position, velocity, acceleration, and time.

A really cute squid rushes toward a A really cute squid rushes toward a studley octopus. The squid runs east studley octopus. The squid runs east at 6 m/s and the octopus runs at 3.5 at 6 m/s and the octopus runs at 3.5 m/s westward. How far does the m/s westward. How far does the octopus get before they run into each octopus get before they run into each other, if they start out 22 m apart?other, if they start out 22 m apart? S

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Free Fall – the motion of an object falling Free Fall – the motion of an object falling under the influence of gravityunder the influence of gravity

We will ignore air frictionWe will ignore air friction

Time frame is only while the object is in free Time frame is only while the object is in free fallfall

So after release and before it hits the bottomSo after release and before it hits the bottom

Acceleration is 9.80m/sAcceleration is 9.80m/s22 downward, or - downward, or -9.80m/s9.80m/s22

Free Fall Applet

1.6 Freely Falling ObjectsCompare the relationship among position, velocity, acceleration, and time.

Common Things People ForgetCommon Things People Forget Acceleration values do not changeAcceleration values do not change Velocity does changeVelocity does change Velocity can be zero, even if the Velocity can be zero, even if the

acceleration is notacceleration is not Negative means downwardNegative means downward

1.6 Freely Falling ObjectsCompare the relationship among position, velocity, acceleration, and time.

A skunk named Fred is thrown upward with A skunk named Fred is thrown upward with an initial velocity of 25 m/s. He tries to an initial velocity of 25 m/s. He tries to catch an apple off a tree as he passes by. catch an apple off a tree as he passes by. How many seconds does he have to get How many seconds does he have to get ready to grab, if the apple is 10 m above ready to grab, if the apple is 10 m above the ground?the ground? S

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Super pig goes charging down the road in his Super pig goes charging down the road in his super pig mobile.super pig mobile.

If he is traveling at 20m/s If he is traveling at 20m/s

and is chasing an eviland is chasing an evil

villain who has a 100 mvillain who has a 100 m

head start and travelinghead start and traveling

at a constant 30 m per second, how fast must at a constant 30 m per second, how fast must

the pig-mobile accelerate to catch him in 35 the pig-mobile accelerate to catch him in 35

seconds?seconds?

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A vicious attack bunny jumps at you from A vicious attack bunny jumps at you from behind your behind your

neighbor’s bushes. neighbor’s bushes. You start from rest and run with an You start from rest and run with an acceleration of 5 m/sacceleration of 5 m/s22.. .. In the distance (75m) you see a tree you In the distance (75m) you see a tree you

can climb. can climb. The bunny freezes for 1.5 s, then The bunny freezes for 1.5 s, then

accelerates at 10 m/saccelerates at 10 m/s22. Do you make it . Do you make it to safety?to safety?

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A giant chicken is racing a A giant chicken is racing a

dinosaur. If the chicken dinosaur. If the chicken

has a 20 m head start and has a 20 m head start and

accelerates from rest at accelerates from rest at

3.0 m/s3.0 m/s22, and the , and the

dinosaur starts from rest dinosaur starts from rest

5s later accelerating at 7.0 m/s5s later accelerating at 7.0 m/s22, how , how

long has the chicken been running before long has the chicken been running before it gets caught?it gets caught?

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A really happy camel is A really happy camel is running at 25 m/s through running at 25 m/s through the desert when he sees a the desert when he sees a large berry bush. He large berry bush. He slams on his brakes and accelerates at -3.5 slams on his brakes and accelerates at -3.5 m/sm/s22 for 12 seconds. If the berry bush was for 12 seconds. If the berry bush was 100 m in front of him, how far is the bush 100 m in front of him, how far is the bush and what is his velocity relative to the bush and what is his velocity relative to the bush at the end of the time period?at the end of the time period?

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A vicious swan is A vicious swan is

chasing a dog. The chasing a dog. The

dog swims at a dog swims at a constant 3 m/s and the swan constant 3 m/s and the swan accelerates from 1 m/s at 2m/saccelerates from 1 m/s at 2m/s22. .

How long will it take the swan to catch the How long will it take the swan to catch the dog. The dog starts out with a 5 m dog. The dog starts out with a 5 m head start, but they both run for the head start, but they both run for the same amount of time.same amount of time.

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