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CP PhysicsCP PhysicsUnit 1 Unit 1

KinematicsKinematicsThe Physics of MotionThe Physics of Motion

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KinematicsKinematics

KinematicsKinematics is the science of describing is the science of describing the motion of objects using words, the motion of objects using words, diagrams, numbers, graphs, and diagrams, numbers, graphs, and equations. equations.

The goal of any study of kinematics is to The goal of any study of kinematics is to develop sophisticated mental models develop sophisticated mental models which serve us in describing (and which serve us in describing (and ultimately, explaining) the motion of ultimately, explaining) the motion of real-world objects. real-world objects.

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KinematicsKinematics In this lesson, we will investigate the words In this lesson, we will investigate the words

used to describe the motion of objects. That used to describe the motion of objects. That is, we will focus on the is, we will focus on the languagelanguage of of kinematics. kinematics.

The words listed below are used with The words listed below are used with regularity to describe the motion of objects. regularity to describe the motion of objects. Your goal should be to become very familiar Your goal should be to become very familiar with their meanings.with their meanings.

vectors, scalars, distance, displacement, speed, velocity, acceleration.

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Vectors and ScalarsVectors and Scalars

The motion of The motion of objects can be objects can be described by described by words which words which represent represent mathematical mathematical quantities.quantities.

ScalarsScalars are are quantities which quantities which are fully are fully described by a described by a magnitude alone. magnitude alone.

VectorsVectors are are quantities which quantities which are fully are fully described by described by both a magnitude both a magnitude and a direction.and a direction.

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ExamplesExamples

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Distance and Distance and DisplacementDisplacement

Distance and Distance and displacement are displacement are two quantities two quantities which may seem to which may seem to mean the same mean the same thing, yet have thing, yet have distinctly different distinctly different definitions and definitions and meanings.meanings.

DistanceDistance is a is a scalar quantity which refers to "how much ground an object has covered" during its motion.

DisplacementDisplacement is a is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.

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Distance and Distance and DisplacementDisplacement

To test your To test your understanding of this understanding of this distinction, consider distinction, consider the following motion the following motion depicted in the depicted in the diagram.diagram.

A physics teacher A physics teacher walks 4 meters East, walks 4 meters East, 2 meters South, 4 2 meters South, 4 meters West, and meters West, and finally 2 meters finally 2 meters North.North.

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AnswerAnswer

Even though the physics teacher has Even though the physics teacher has walked a total walked a total distance distance of 12 of 12 meters, her meters, her displacementdisplacement is 0 is 0 meters. meters.

The 4 meters east is The 4 meters east is canceledcanceled by the by the 4 meters west; and the 2 meters 4 meters west; and the 2 meters south is south is canceledcanceled by the 2 meters by the 2 meters north.north.

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SummarySummary To understand the distinction between To understand the distinction between

distance and displacement, you must distance and displacement, you must know the definitions and also know that a know the definitions and also know that a vector quantity such as displacement is direction-awaredirection-aware and a and a scalar quantity such as distance is ignorant of directionignorant of direction. .

When an object changes its direction of When an object changes its direction of motion, displacement takes this direction motion, displacement takes this direction change into account; heading the opposite change into account; heading the opposite direction effectively begins to direction effectively begins to cancel cancel whatever displacement there once was.whatever displacement there once was.

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Now consider another example. The diagram below Now consider another example. The diagram below shows the position of a cross-country skier at shows the position of a cross-country skier at various times. various times.

Use the diagram to determine the resulting Use the diagram to determine the resulting displacement and the distance traveled by the skier displacement and the distance traveled by the skier during these three minutes. during these three minutes.

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Speed and VelocitySpeed and Velocity Just as distance and Just as distance and

displacement have displacement have distinctly different distinctly different meanings (despite meanings (despite their similarities), so their similarities), so do do speedspeed and and velocityvelocity. .

VelocityVelocity is a is a vector quantity which refers to "the rate at which an object changes its position."

SpeedSpeed is a is a scalar quantity which refers to "how fast an object is moving."

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VelocityVelocity

The direction of The direction of the velocity vector the velocity vector is simply the same is simply the same as the direction as the direction which an object is which an object is moving. moving.

It would not matter It would not matter whether the object is whether the object is speeding up or slowing speeding up or slowing down, if the object is down, if the object is moving rightwards, then moving rightwards, then its velocity is described its velocity is described as being rightwards. as being rightwards.

If an object is moving If an object is moving downwards, then its downwards, then its velocity is described as velocity is described as being downwards. being downwards.

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Calculating Average Speed Calculating Average Speed and Velocityand Velocity

The average speed The average speed during the course during the course of a motion can be of a motion can be solved by using the solved by using the following equation:following equation:

Meanwhile, the Meanwhile, the average velocity is average velocity is often solved using often solved using the equation.the equation.

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Average Speed Average Speed Here’s an example:Here’s an example:

While on While on vacation, Lisa vacation, Lisa Carr traveled a Carr traveled a total distance of total distance of 440 miles. Her 440 miles. Her trip took 8 hours. trip took 8 hours. What was her What was her average speed?average speed?

To compute her To compute her average speed, we average speed, we simply divide the simply divide the distance of travel distance of travel by the time of by the time of travel.travel.

€

speed =distance

time=440mi

8hr= 55mi /hr

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Average Speed vs. Average Speed vs. Instantaneous SpeedInstantaneous Speed

Since a moving Since a moving object often changes object often changes its speed during its its speed during its motion, it is common motion, it is common to distinguish to distinguish between the average between the average speed and the speed and the instantaneous instantaneous speed. The speed. The distinction is as distinction is as follows. follows.

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Average vs. Average vs. InstantaneousInstantaneous

Instantaneous Instantaneous SpeedSpeed - speed at - speed at any given instant any given instant in time. in time.

Average SpeedAverage Speed - - average of all average of all instantaneous instantaneous speeds; found speeds; found simply by a simply by a distance/time ratio.distance/time ratio.

You might think of You might think of the instantaneous the instantaneous speed as the speed speed as the speed which the which the speedometer reads at speedometer reads at any given instant in any given instant in time and the average time and the average speed as the average speed as the average of all the of all the speedometer speedometer readings during the readings during the course of the trip. course of the trip.

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Constant SpeedConstant Speed

Moving objects don't always travel Moving objects don't always travel with erratic and changing speeds. with erratic and changing speeds. Occasionally, an object will move at Occasionally, an object will move at a steady rate with a constant speed. a steady rate with a constant speed.

That is, the object will cover the That is, the object will cover the same distance every regular interval same distance every regular interval of time. of time.

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Constant vs. ChangingConstant vs. Changing

The data tables below depict objects The data tables below depict objects with constant and changing speed. with constant and changing speed.

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Now let's try a little more difficult case by Now let's try a little more difficult case by considering the motion of considering the motion of that physics teacher again. The physics teacher walks 4 meters East, 2 meters . The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. The entire motion lasted for 24 seconds. Determine Determine the average speed and the average velocity.the average speed and the average velocity.

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Average speed and Average speed and velocityvelocity

The physics teacher walked a The physics teacher walked a distance of 12 meters in 24 seconds; thus, her of 12 meters in 24 seconds; thus, her average speed was 0.50 m/s. average speed was 0.50 m/s.

However, since her displacement is 0 However, since her displacement is 0 meters, her average velocity is 0 m/s. meters, her average velocity is 0 m/s. Remember that the displacement Remember that the displacement refers to the change in position and refers to the change in position and the velocity is based upon this the velocity is based upon this position change. position change.

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Here is another example similar to Here is another example similar to what was seen before in the what was seen before in the discussion of distance and discussion of distance and displacement. displacement.

Use the diagram to determine the Use the diagram to determine the average speed and the average average speed and the average velocityvelocity of the skier during these of the skier during these three minutes. three minutes.

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AccelerationAcceleration

The final mathematical quantity The final mathematical quantity discussed is acceleration. discussed is acceleration.

AccelerationAcceleration is a vector quantity is a vector quantity which is defined as "the rate at which is defined as "the rate at which an object changes its which an object changes its velocity." An object is accelerating if velocity." An object is accelerating if it is changing its velocity. it is changing its velocity.

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Acceleration has to do with changing Acceleration has to do with changing how fast an object is moving. If an how fast an object is moving. If an object is not changing its velocity, object is not changing its velocity, then the object is not accelerating. then the object is not accelerating.

The data below is representative of a The data below is representative of a northward-moving accelerating northward-moving accelerating object - the velocity is changing with object - the velocity is changing with respect to time. respect to time.

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Constant AccelerationConstant Acceleration

Sometimes an accelerating object Sometimes an accelerating object will change its velocity by the same will change its velocity by the same amount each second. See previous amount each second. See previous example. This is known as example. This is known as Constant Constant Acceleration.Acceleration.

An object with a constant An object with a constant acceleration should not be confused acceleration should not be confused with an object with a constant with an object with a constant velocity. Don't be fooled! velocity. Don't be fooled!

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The data tables below depict The data tables below depict motions of objects with a constant motions of objects with a constant acceleration and a changing acceleration and a changing acceleration. Note that each object acceleration. Note that each object has a changing velocity. has a changing velocity.

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Free Fall Free Fall

Since accelerating objects are constantly Since accelerating objects are constantly changing their velocity, one can say that the changing their velocity, one can say that the distance traveled/time is not a constant distance traveled/time is not a constant value. If we were to observe the motion of a value. If we were to observe the motion of a free-falling objectfree-falling object we would observe a we would observe a constant acceleration.constant acceleration.

Check out the following data.Check out the following data. This data illustrates that a free-falling object This data illustrates that a free-falling object

which is accelerating at a constant rate will which is accelerating at a constant rate will cover different distances in each consecutive cover different distances in each consecutive second. second.

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Time Time intervalinterval

Ave. Ave. Velocity Velocity during during time time intervalinterval

Distance Distance traveled traveled during during time time intervalinterval

Total Total Distance Distance Traveled Traveled from 0 s from 0 s to End to End of Time of Time IntervalInterval

0-1s0-1s 5m/s5m/s 5 m5 m 5 m5 m

1-2s1-2s 15m/s15m/s 15 m15 m 20 m20 m

2-3s2-3s 25m/s25m/s 25 m25 m 45 m45 m

3-4s3-4s 35m/s35m/s 35 m35 m 80 m80 m

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Calculating average Calculating average accelerationacceleration

The average acceleration of any object over a The average acceleration of any object over a given interval of time can be calculated using given interval of time can be calculated using the equationthe equation

This equation can be used to calculate the This equation can be used to calculate the acceleration of the object whose motion is acceleration of the object whose motion is depicted by the velocity-time data table above. depicted by the velocity-time data table above. The velocity-time data in the table shows that The velocity-time data in the table shows that the object has an acceleration of 10 m/s/s. the object has an acceleration of 10 m/s/s.

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The Direction of the The Direction of the Acceleration Vector Acceleration Vector

Since acceleration is a vector Since acceleration is a vector quantity, it will always have a quantity, it will always have a direction associated with it. The direction associated with it. The direction of the acceleration vector direction of the acceleration vector depends on two things:depends on two things:

1.1. whether the object is speeding up whether the object is speeding up or slowing down or slowing down

2.2. whether the object is moving in the whether the object is moving in the + or - direction + or - direction

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Acceleration VectorAcceleration Vector

The general RULE OF THUMB is:The general RULE OF THUMB is: If an object is slowing down, then its If an object is slowing down, then its

acceleration is in the opposite acceleration is in the opposite direction of its motion. direction of its motion.

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Direction of AccelerationDirection of Acceleration

Negative accelerationNegative acceleration

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Check your Check your understandingunderstanding

Use the equation for acceleration to Use the equation for acceleration to determine the acceleration for the determine the acceleration for the following two motions. following two motions.

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Describing Motion with Describing Motion with DiagramsDiagrams

Like the study of all of physics, Like the study of all of physics, our study of kinematics will be our study of kinematics will be concerned with the multiple concerned with the multiple means by which the motion of means by which the motion of objects can be represented. objects can be represented.

Such means include the use of Such means include the use of words, the use of graphs, the use words, the use of graphs, the use of numbers, the use of equations, of numbers, the use of equations, and the use of diagrams. and the use of diagrams.

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Describing motionDescribing motion

The two most The two most commonly used commonly used types of diagrams types of diagrams used to describe used to describe the motion of the motion of objects are:objects are:

- ticker tape - ticker tape diagramsdiagrams

- vector diagrams- vector diagrams

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Ticker Tape Diagrams or Ticker Tape Diagrams or Oil Drop DiagramsOil Drop Diagrams

The distance between dots on a The distance between dots on a ticker tape represents the ticker tape represents the object's position change during object's position change during that time interval.that time interval.

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AccelerationAcceleration

The analysis of a ticker tape The analysis of a ticker tape diagram will also reveal if the diagram will also reveal if the object is moving with a constant object is moving with a constant velocity or accelerating. velocity or accelerating.

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Vector DiagramsVector Diagrams

Vector diagramsVector diagrams are diagrams are diagrams which depict the direction and which depict the direction and relative magnitude of a vector relative magnitude of a vector quantity by a vector arrow. quantity by a vector arrow.

Vector diagrams can be used to Vector diagrams can be used to describe the velocity of a moving describe the velocity of a moving object during its motion. object during its motion.

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VectorsVectors

In a vector diagram, the magnitude In a vector diagram, the magnitude of a vector is represented by the of a vector is represented by the size of the vector arrow. size of the vector arrow.

If the size of the arrow in each If the size of the arrow in each consecutive frame of the vector consecutive frame of the vector diagram is the same, then the diagram is the same, then the magnitude of that vector is magnitude of that vector is constant. constant.

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