Unit 3:Unit 3:One Dimensional One Dimensional KinematicsKinematics

Section A: Velocity and Section A: Velocity and AccelerationAcceleration

Corresponding Book Sections:Corresponding Book Sections:– 2.2, 2.42.2, 2.4

PA Assessment Anchors:PA Assessment Anchors:– S11.C.3S11.C.3

What is kinematics?What is kinematics?

KinematicsKinematics– The study of motion and how to describe The study of motion and how to describe

itit– Does not consider what causes the Does not consider what causes the

motionmotion

One Dimensional (1D) KinematicsOne Dimensional (1D) Kinematics– Motion in a straight lineMotion in a straight line

Left/right, up/down, east/west, etcLeft/right, up/down, east/west, etc

Coordinate systemCoordinate system

Defines position of an objectDefines position of an object

xf xi x = 0

+

Indicates the positivedirection

Basics of a coordinate Basics of a coordinate systemsystem

Establish a positive directionEstablish a positive direction

Establish an origin (0 point)Establish an origin (0 point)

The origin and positive direction The origin and positive direction must remain the same for the entire must remain the same for the entire problemproblem

Sample ProblemSample Problem

Page 17, Figure 2-2Page 17, Figure 2-2

Set up a coordinate systemSet up a coordinate system– Choose your own originChoose your own origin– Choose the positive directionChoose the positive direction

Distance vs. DisplacementDistance vs. Displacement

DistanceDistance– Total length of travelTotal length of travel– Units: m, cm, mm, kmUnits: m, cm, mm, km

DisplacementDisplacement– Change in position = final - initialChange in position = final - initial x = xx = xff - x - xii

Greek letter “delta”…stands for “Change in”

Back to the sample Back to the sample problem…problem…

Page 17, Figure 2-2Page 17, Figure 2-2

If you leave your friend’s house, go If you leave your friend’s house, go to the supermarket, and come home, to the supermarket, and come home, find the:find the:– DistanceDistance– DisplacementDisplacement

Another example…Another example…

Suppose you leave the grocery store, Suppose you leave the grocery store, stop at your house, go back to the stop at your house, go back to the grocery store, and then go to your grocery store, and then go to your friend’s house. Find the:friend’s house. Find the:– DistanceDistance– DisplacementDisplacement

Last example…Last example…

Suppose you walk from the grocery Suppose you walk from the grocery store to your friend’s house. Find store to your friend’s house. Find the:the:– DistanceDistance– DisplacementDisplacement

What does the negative What does the negative mean?mean?

Remember that we set a certain Remember that we set a certain direction as positive…direction as positive…– Getting a negative simply means that Getting a negative simply means that

we are in the opposite direction as the we are in the opposite direction as the one we established as positiveone we established as positive

– This DOES NOT mean that a negative This DOES NOT mean that a negative number is less than a positive valuenumber is less than a positive value

Before we go any further…Before we go any further…

We need to consistently set up We need to consistently set up problems to make sure we’re problems to make sure we’re following the right steps and make following the right steps and make our work clearour work clear

(And to receive full credit (And to receive full credit ))

Sample Problem SetupSample Problem Setup

Sketch of the Problem

Data Table

ValuesUnknown Variables

Ex:t = 3s

xi = 5 mxf = ?

All Work

Equations UsedStep by-step derivations

(Not division, multiplication, etc)

It takes practice…It takes practice…

It will take practice to start setting up It will take practice to start setting up problems (and not just jumping in to problems (and not just jumping in to solving them)solving them)

In the end, you’ll be more accurateIn the end, you’ll be more accurate

You MUST set up problems like this You MUST set up problems like this on ALL tests, homework assignments, on ALL tests, homework assignments, classwork, etc to receive full credit!classwork, etc to receive full credit!

Speed vs. VelocitySpeed vs. Velocity

SpeedSpeed– Rate of motionRate of motion

– Units: m/s, km/hrUnits: m/s, km/hr

VelocityVelocity– Displacement per Displacement per

unit of timeunit of time

– Units: m/s, km/hrUnits: m/s, km/hr WITH a directionWITH a direction

– N, S, E, W, etcN, S, E, W, etc– + or --+ or --

distanceAverage Speed =

timedisplacement

Average Velocity = time

Sample ProblemSample Problem

You drive 4.0 hr at 30.0 mph and You drive 4.0 hr at 30.0 mph and then another 4.0 hr at 50 mph. Is then another 4.0 hr at 50 mph. Is your average speed:your average speed:– Greater than 40 mphGreater than 40 mph– Equal to 40 mphEqual to 40 mph– Less than 40 mphLess than 40 mph

Find average speed and Find average speed and average velocity for each part average velocity for each part

of the tripof the trip

t = 10 s

t = 50 s

One way to look at One way to look at position vs. time…position vs. time…

Another way…Another way…

Practice problem #1Practice problem #1

Draw a position vs. time graph for Draw a position vs. time graph for the following situation:the following situation:– You walk 2 m from your house in 3 You walk 2 m from your house in 3

secondsseconds– You walk another 3 m in 5 secondsYou walk another 3 m in 5 seconds– You stop for 4 seconds to restYou stop for 4 seconds to rest– You turn around and walk back to your You turn around and walk back to your

house in 6 secondshouse in 6 seconds

Answer…Answer…

Practice problem #2Practice problem #2

Draw a position vs. time graph for Draw a position vs. time graph for the following situation:the following situation:– You walk 10 m toward the school in 5 You walk 10 m toward the school in 5

secondsseconds– You stop to answer your phone for 10 You stop to answer your phone for 10

secondsseconds– You walk back to your car in 5 secondsYou walk back to your car in 5 seconds– You’re late for 1You’re late for 1stst pd, so you walk to the pd, so you walk to the

10 m to school in 3 seconds.10 m to school in 3 seconds.

Answer…Answer…

Instantaneous Speed & Instantaneous Speed & VelocityVelocity

Instantaneous Instantaneous SpeedSpeed– Magnitude of the Magnitude of the

instantaneous instantaneous velocityvelocity

Instantaneous Instantaneous Velocity Velocity – Velocity at one Velocity at one

instant in timeinstant in time

– Unit: m/sUnit: m/s

Speedometer QuestionSpeedometer Question

What does a car’s speedometer What does a car’s speedometer measure?measure?– Average SpeedAverage Speed– Average VelocityAverage Velocity– Instantaneous SpeedInstantaneous Speed– Instantaneous VelocityInstantaneous Velocity

Explain.Explain.

AccelerationAcceleration

The change of velocity with timeThe change of velocity with time

Units: m/sUnits: m/s22, mph/s, etc…, mph/s, etc…

Practice Problem #1Practice Problem #1

Saab advertises a car that goes from Saab advertises a car that goes from 0 to 60 mph in 6.2 seconds. Find the 0 to 60 mph in 6.2 seconds. Find the average acceleration.average acceleration.

Practice Problem #2Practice Problem #2

An airplane has an average An airplane has an average acceleration of 5.6 m/sacceleration of 5.6 m/s22 during during takeoff. How long does it take for takeoff. How long does it take for the plane to reach a speed of 150 the plane to reach a speed of 150 mph?mph?

Acceleration vs. Acceleration vs. DecelerationDeceleration

AccelerationAcceleration– Final speed > Initial Final speed > Initial

SpeedSpeed

DecelerationDeceleration– Final speed < Initial Final speed < Initial

SpeedSpeed

Connection between Connection between acceleration and velocityacceleration and velocity

Situation 1:Situation 1:– Acceleration and Acceleration and

velocity in same velocity in same directiondirection

– Speed of object Speed of object increasesincreases

Situation 2:Situation 2:– Acceleration and Acceleration and

velocity in different velocity in different directionsdirections

– Speed of object Speed of object decreasesdecreases

Practice Problem #1Practice Problem #1

A ferry makes a short run between A ferry makes a short run between two docks. As the ferry approaches two docks. As the ferry approaches the dock (positive x-direction), it has the dock (positive x-direction), it has a speed of 7.4 m/s and slows down to a speed of 7.4 m/s and slows down to a stop in 12.3 s. Find the a stop in 12.3 s. Find the acceleration.acceleration.

Practice Problem #2Practice Problem #2

The ferry now leaves the dock As The ferry now leaves the dock As the ferry approaches the dock, it has the ferry approaches the dock, it has a speed of 7.3 m/s and now slows a speed of 7.3 m/s and now slows down to a stop in 13.1 s. Find the down to a stop in 13.1 s. Find the acceleration.acceleration.

Hint: Think about positive/negative Hint: Think about positive/negative

direction based on last problemdirection based on last problem

The most important The most important acceleration…acceleration…

Recall from other science classes that Recall from other science classes that gravity is always pulling down on gravity is always pulling down on everything.everything.

Gravity has an acceleration Gravity has an acceleration represented by: represented by: gg

gg = 9.81 m/s = 9.81 m/s22 You need to use this exact value

Section B: Kinematics Section B: Kinematics EquationsEquations

Corresponding Book Sections:Corresponding Book Sections:– 2.5, 2.6, 2.72.5, 2.6, 2.7

PA Assessment Anchors:PA Assessment Anchors:– S11.C.3S11.C.3

Motion with Constant Motion with Constant AccelerationAcceleration

Object is either speeding up or Object is either speeding up or slowing downslowing down

Object is just speeding up / slowing Object is just speeding up / slowing down at a constant rate (same down at a constant rate (same acceleration at all times)acceleration at all times)

Velocity as a function of time:

Position as a function of time:

Velocity as a function of position:

Kinematics EquationsKinematics Equations

How do I know when How do I know when to use each equation?to use each equation?

That’s where the sketch and data That’s where the sketch and data table will come in handy…table will come in handy…

Look at what you have, what you’re Look at what you have, what you’re looking for, and find the equation looking for, and find the equation that will include all of those variablesthat will include all of those variables

You may need to use more than one You may need to use more than one equation in a problemequation in a problem

Practice Problem #1Practice Problem #1

A ball is thrown straight upward with A ball is thrown straight upward with an initial velocity of 8.2 m/s. If the an initial velocity of 8.2 m/s. If the acceleration of the ball is that of acceleration of the ball is that of gravity, find the velocity after:gravity, find the velocity after:– 0.50 s0.50 s– 1.0 s1.0 s

Practice Problem #2Practice Problem #2

A boat moves slowly inside a marina A boat moves slowly inside a marina with a constant speed of 1.50 m/s. with a constant speed of 1.50 m/s. As soon as it leaves the marina, it As soon as it leaves the marina, it accelerates at 2.40 m/saccelerates at 2.40 m/s22. Find the:. Find the:– Speed it’s moving after 5.0 sSpeed it’s moving after 5.0 s– Distance it’s traveled after 5.0 s of Distance it’s traveled after 5.0 s of

accelerationacceleration

Practice Problem #3Practice Problem #3

A drag racer starts from rest and A drag racer starts from rest and accelerates at 7.40 m/saccelerates at 7.40 m/s22. How far . How far has it traveled in:has it traveled in:– 1.0 s1.0 s– 2.0 s2.0 s– 3.0 s3.0 s

Review of the Equations…Review of the Equations…

Freely Falling ObjectsFreely Falling Objects

Free Fall -- the motion of an object falling Free Fall -- the motion of an object falling onlyonly under the influence of gravity. under the influence of gravity.

An object is in free fall the moment it is An object is in free fall the moment it is released, whether it’s thrown upward, released, whether it’s thrown upward, downward, or just dropped.downward, or just dropped.

Why don’t we have true free fall on Why don’t we have true free fall on Earth?Earth?

Consider…Consider…

More on gravityMore on gravity Remember…Remember…

– Acceleration due to gravity = Acceleration due to gravity = gg = 9.81 m/s = 9.81 m/s22

That value will be:That value will be:– Positive if our coordinate system has set down as Positive if our coordinate system has set down as

positivepositive

– Negative if our coordinate system has set up as Negative if our coordinate system has set up as positivepositive

Gravity ALWAYS acts in the downward Gravity ALWAYS acts in the downward direction.direction.

+

+

Free Free fall fall

from from restrest

Projectile MotionProjectile Motion