+ unit 3: one dimensional kinematics. + section a: velocity and acceleration corresponding book...

+Unit 3:One Dimensional Kinematics

+Section A: Velocity and Acceleration

Corresponding Book Sections:2.2, 2.4

PA Assessment Anchors:S11.C.3

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+What is kinematics?

KinematicsThe study of motion and how to describe it

Does not consider what causes the motion

One Dimensional (1D) KinematicsMotion in a straight line

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

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+Coordinate system

Defines position of an object

xf xi x = 0

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Indicates the positivedirection

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+Basics of a coordinate system

Establish a positive direction

Establish an origin (0 point)

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

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+Sample Problem

Page 17, Figure 2-2

Set up a coordinate systemChoose your own originChoose the positive direction

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+Distance vs. Displacement

DistanceTotal length of travelUnits: m, cm, mm, km

DisplacementChange in position = final - initial x = xf - xi

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

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+Back to the sample problem…

Page 17, Figure 2-2

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

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+Another example…

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

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+Last example…

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

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+What does the negative mean?

Remember that we set a certain direction as positive…Getting a negative simply means that we are in the opposite direction as the one we established as positive

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

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+Before we go any further…

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

(And to receive full credit )

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+Sample 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)

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+It takes practice…

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

In the end, you’ll be more accurate

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

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+Speed vs. Velocity

SpeedRate of motion

Units: m/s, km/hr

Velocity Displacement per unit of time

Units: m/s, km/hrWITH a direction

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

distanceAverage Speed =

time displacementAverage Velocity =

time

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+Sample Problem

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

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

t = 10 s

t = 50 s

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+Position vs. Time Graph18

+Practice problem #1

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

You walk another 3 m in 5 secondsYou stop for 4 seconds to restYou turn around and walk back to your house in 6 seconds

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+Answer…

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+Practice problem #2

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

You stop to answer your phone for 10 seconds

You walk back to your car in 5 seconds

You’re late for 1st pd, so you walk to the 10 m to school in 3 seconds.

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+Answer…

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+Instantaneous Speed & Velocity

Instantaneous SpeedMagnitude of the instantaneous velocity

Instantaneous Velocity Velocity at one instant in time

Unit: m/s

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+Speedometer Question

What does a car’s speedometer measure?Average SpeedAverage VelocityInstantaneous SpeedInstantaneous Velocity

Explain.

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+Acceleration

The change of velocity with time

Units: m/s2, mph/s, etc…

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+Practice Problem #1

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

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+Practice Problem #2

An airplane has an average acceleration of 5.6 m/s2 during takeoff. How long does it take for the plane to reach a speed of 150 mph?

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+Acceleration vs. Deceleration

AccelerationFinal speed > Initial Speed

DecelerationFinal speed < Initial Speed

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Connection between acceleration and velocity Situation 1:

Acceleration and velocity in same direction

Speed of object increases

Situation 2: Acceleration and velocity in different directions

Speed of object decreases

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+Practice Problem #1

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

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+Practice Problem #2

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

Hint: Think about positive/negative

direction based on last problem

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+The most important acceleration…Recall from other science classes that gravity is always pulling down on everything.

Gravity has an acceleration represented by: g

g = 9.8 m/s2

You need to use this exact value

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+Section B: Kinematics Equations

Corresponding Book Sections:2.5, 2.6, 2.7

PA Assessment Anchors:S11.C.3

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+Motion with Constant AccelerationObject is either speeding up or slowing down

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

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+

Velocity as a function of time:

Position as a function of time:

Velocity as a function of position:

Kinematics Equations35

+How do I know when to use each equation?That’s where the sketch and data table will come in handy…

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

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

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+Practice Problem #1

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

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+Practice Problem #2

A boat moves slowly inside a marina with a constant speed of 1.50 m/s. As soon as it leaves the marina, it accelerates at 2.40 m/s2. Find the:Speed it’s moving after 5.0 sDistance it’s traveled after 5.0 s of acceleration

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+Practice Problem #3

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

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+Review of the Equations…

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+Freely Falling Objects

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

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

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

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+Consider…

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+More on gravity

Remember… Acceleration due to gravity = g = 9.81 m/s2

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

Negative if our coordinate system has set up as positive

Gravity ALWAYS acts in the downward direction.

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+Free fall from rest

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+Projectile Motion

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