Fill in the missing bubble…. Kinematics in One Dimension Chapter 2

Fill in the missing bubble…Fill in the missing bubble…

Kinematics in One Kinematics in One DimensionDimension

Chapter 2Chapter 2

Kin-e-what?Kin-e-what?

KinematicsKinematics – the branch of – the branch of __________________ which which describes the motion of an object without describes the motion of an object without explicit reference to the ______ that act on the explicit reference to the ______ that act on the object.object.

MechanicsMechanics – the branch of Physics that deals – the branch of Physics that deals with the ______ of objects and the ______ that with the ______ of objects and the ______ that change it.change it.

One DimensionOne Dimension – dealing only with ________ – dealing only with ________ motion.motion.

mechanics

forces

motion forces

linear

Familiar terms?Familiar terms? Can you define the following? Take a minute Can you define the following? Take a minute

to write down your answer, then, using the to write down your answer, then, using the same groups for the poster, votefor the same groups for the poster, votefor the ‘‘bestbest’’ choice. DO NOT look in in your book!choice. DO NOT look in in your book! DisplacementDisplacement VelocityVelocity AccelerationAcceleration

Alright, letAlright, let’’s share…s share…

So what do they really mean?So what do they really mean?SP1. a1Determine the difference between distnace and SP1. a1Determine the difference between distnace and displacementdisplacement

SP1.a2 Identify the displacement, time and velocity [s, t, SP1.a2 Identify the displacement, time and velocity [s, t, v]v]DisplacementDisplacement (s) is similar to distance. It is, in general, the (s) is similar to distance. It is, in general, the change in position of an object. change in position of an object. Answers the question Answers the question ““How farHow far””..DistanceDistance is the total amount from the beginning of travel is the total amount from the beginning of travelDisplacementDisplacement is always measured from the origin to the is always measured from the origin to the current position.current position.Student walking around demo!!Student walking around demo!!

So what do they really mean?So what do they really mean?SP1.a4 Describe the difference between speed and SP1.a4 Describe the difference between speed and

velocity [speed, vvelocity [speed, vavgavg]]

VelocityVelocity (v (vavgavg) is similar to _________ (again, ) is similar to _________ (again,

difference later). It is defined as the change in difference later). It is defined as the change in displacement divided by time. displacement divided by time.

Answers the question Answers the question ““How FastHow Fast”” Speed does not care about directionSpeed does not care about direction Velocity changes as direction changesVelocity changes as direction changes Can you write the equation?Can you write the equation?

speed

So what do they really mean?So what do they really mean?

SP1.a3 Calculate the velocity of an object. SP1.a3 Calculate the velocity of an object. [v=s/t] [v=s/t] That equation would be That equation would be

This is called a definition equation. You will This is called a definition equation. You will use it to derive other equations in this course.use it to derive other equations in this course.Do you see what the units would be?Do you see what the units would be?


SP1.a6 Calculate the acceleration of an object.SP1.a6 Calculate the acceleration of an object.AccelerationAcceleration (a) is the change in ________ of an (a) is the change in ________ of an object divided by the time interval. object divided by the time interval. You must do one of 3 things:You must do one of 3 things:

Increase velocityIncrease velocity Decrease velocityDecrease velocity Change directionChange direction

If there is no speed change or direction change, If there is no speed change or direction change, there is NO ACCELERATION.there is NO ACCELERATION.Can you write the equation?Can you write the equation?

velocity


Did you getDid you get

Again, another definition equation.Again, another definition equation. Special Note: Very rarely does time NOT Special Note: Very rarely does time NOT

begin at zero. Therefore, it is very common to begin at zero. Therefore, it is very common to write these equations without the write these equations without the ΔΔ symbol by symbol by time.time.

Looking deeper at DisplacementLooking deeper at Displacement

Can you answer the following questions? Can you answer the following questions? (avoid using your calculator)(avoid using your calculator)

1.1. A student walks 15 m from the commons, A student walks 15 m from the commons, stops at her locker, then continues 20 m to stops at her locker, then continues 20 m to her classroom. What is her displacement?her classroom. What is her displacement?

2.2. Another student walks 30 m from the Another student walks 30 m from the commons before realizing he meant to stop commons before realizing he meant to stop at his locker. He returns 10 m to his locker, at his locker. He returns 10 m to his locker, then turns back toward his class, 20 m from then turns back toward his class, 20 m from his locker. What is his displacement?his locker. What is his displacement?

35 m

40 m

Looking Deeper at DisplacementLooking Deeper at Displacement

SP1.b1 Describe and identiy scalar and vector SP1.b1 Describe and identiy scalar and vector quantities quantities So what makes the difference between 60 m or 40 m So what makes the difference between 60 m or 40 m for question #2?for question #2?The difference is that 60 m is the The difference is that 60 m is the distancedistance the student the student travels (a ______ qty), but 40 m is the travels (a ______ qty), but 40 m is the displacementdisplacement (a (a ______ qty).______ qty).Vectors take into account the direction of motion. In Vectors take into account the direction of motion. In #2 there was a change of direction. Mathematically, #2 there was a change of direction. Mathematically, this is a change in sign for the number. So… 30 m + this is a change in sign for the number. So… 30 m + (-10 m) + 20 m(-10 m) + 20 m

scalarvector

Looking Deeper at VelocityLooking Deeper at Velocity

Okay, explanation first this time. Okay, explanation first this time. Speed is the scalar Speed is the scalar qty for velocity. So, speed is magnitude only (just a qty for velocity. So, speed is magnitude only (just a number). Velocity is magnitude number). Velocity is magnitude andand direction. direction.

Two other terms to note: Two other terms to note: ___________ Velocity = v right now ___________ Velocity = v right now _______ Velocity = overall v: (v = (v_______ Velocity = overall v: (v = (v ff + v + vii)/2))/2)

Remember, a + or – count as direction. You do not Remember, a + or – count as direction. You do not have to say north, south, toward, away, etc., but you have to say north, south, toward, away, etc., but you may see them in a question.may see them in a question.

InstantaneousAverage

Looking Deeper at VelocityLooking Deeper at VelocityAlright, try these two questions on for size:Alright, try these two questions on for size:1.1. A driver traveling north on I-85 notes that it A driver traveling north on I-85 notes that it

takes 2 minutes to get from exit 99 to exit takes 2 minutes to get from exit 99 to exit 101, a distance of 3168 m. What is the 101, a distance of 3168 m. What is the drivers speed in m/s? What is her velocity?drivers speed in m/s? What is her velocity?

2.2. A student walks his girlfriend to 1A student walks his girlfriend to 1stst period, a period, a distance of 40 m from the cafeteria. He turns distance of 40 m from the cafeteria. He turns back toward the cafeteria to his class, 15 m back toward the cafeteria to his class, 15 m away. This takes 5 minutes. What is his away. This takes 5 minutes. What is his speed? His velocity?speed? His velocity?

Speed = 26.4 m/s Velocity = 26.4 m/s

s = 0.18 m/s; v=0.083 m/s

Looking Deeper at AccelerationLooking Deeper at Acceleration Constant acceleration - an object will change its Constant acceleration - an object will change its

velocity by the velocity by the samesame amount each second. amount each second. THIS IS NOT CONSTNAT VELOCITY!!!THIS IS NOT CONSTNAT VELOCITY!!! Non-constant acceleration - an object will change Non-constant acceleration - an object will change

its velocity by its velocity by differentdifferent amounts each second. amounts each second.

Which one is constant? Non-constant?Which one is constant? Non-constant?

Looking Deeper at AccelerationLooking Deeper at Acceleration Since accelerating objects are constantly changing Since accelerating objects are constantly changing

their velocity, one can say that the distance their velocity, one can say that the distance traveled/time is not a constant value. traveled/time is not a constant value.

TimeTime

0 - 1 s0 - 1 s ~ 5 m/s~ 5 m/s ~ 5 m~ 5 m ~ 5 m~ 5 m 1 -2 s1 -2 s~ 15 m/s~ 15 m/s ~ 15 m~ 15 m ~ 20 m~ 20 m 2 - 3 s2 - 3 s ~ 25 m/s~ 25 m/s ~ 25 m~ 25 m ~ 45 m~ 45 m 3 - 4 s3 - 4 s ~ 35 m/s~ 35 m/s ~ 35 m~ 35 m ~ 80 m~ 80 m Lets make 3 quick graphs!Lets make 3 quick graphs!

Velocity

Distance traveled in interval

Total distance traveled

Looking Deeper at AccelerationLooking Deeper at Acceleration

Well, you may be relieved to know that Well, you may be relieved to know that acceleration is a vector qty with no scalar acceleration is a vector qty with no scalar counterpart.counterpart.

So where is the direction?So where is the direction? The direction of the acceleration vector The direction of the acceleration vector

depends on two things:depends on two things: whether the object is speeding up or slowing downwhether the object is speeding up or slowing down whether the object is moving in the + or - directionwhether the object is moving in the + or - direction


A A positive acceleration positive acceleration occurs, when an occurs, when an object is speeding up. Acceleration is in the object is speeding up. Acceleration is in the same direction as the velocity.same direction as the velocity.

A A negative acceleration negative acceleration occurs, when an occurs, when an object is slowing down. Acceleration is in the object is slowing down. Acceleration is in the opposite direction as the velocity. opposite direction as the velocity.


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

*See demo* *See demo*


Which table shows positive acceleration? Which table shows positive acceleration? negative acceleration?negative acceleration?

A is positive, B is negative. A is positive, B is negative.

Practice…Practice…

So… a car traveling at 10 m/s in a straight line So… a car traveling at 10 m/s in a straight line speeds up to 30 m/s in 5.0 s. What is the speeds up to 30 m/s in 5.0 s. What is the average acceleration?average acceleration?

What are we given? What are we given? What are we looking for?What are we looking for?

a = 4.0 m/s2


A shuttle bus slows down with an average A shuttle bus slows down with an average acceleration of –1.8m/sacceleration of –1.8m/s22. How long does it take . How long does it take the bus to slow from 9.0 m/s to a complete stop? the bus to slow from 9.0 m/s to a complete stop?

What are we given? What are we given? What are we looking for?What are we looking for?


Practice makes perfect!!!Practice makes perfect!!!

Represented as graphsRepresented as graphs

WeWe’’ll get to that later….ll get to that later….

Graphing MotionGraphing Motion

Three types of Graphs: D-T, V-T, A-TThree types of Graphs: D-T, V-T, A-T What does slope of each represent?What does slope of each represent?

This covers all the This covers all the ““conceptconcept””, how, how’’s your s your math skill holding up?math skill holding up?

Position vs Time GraphsPosition vs Time Graphs

Position goes on the vertical axisPosition goes on the vertical axis Time is on the horizontal axisTime is on the horizontal axis


What is the position at time 4s? What about 8s?What is the position at time 4s? What about 8s? What is the the avg What is the the avg

velocity? (think back one velocity? (think back one

slide.) slide.) 1 m/s 1 m/s

Position vs Time GraphsPosition vs Time Graphs LetLet’’s consider this car.s consider this car.

The graph would look like this:The graph would look like this: It would have a constant, rightward (+) velocityIt would have a constant, rightward (+) velocity

Position vs Time GraphsPosition vs Time Graphs Now, letNow, let’’s consider this other car.s consider this other car.

It would have a changing rightward (+) velocityIt would have a changing rightward (+) velocity The graph would look like this:The graph would look like this:

Position vs Time GraphsPosition vs Time Graphs The shapes of the position versus time graphs reveal The shapes of the position versus time graphs reveal

reveals useful information about the velocity of the reveals useful information about the velocity of the object. object.

It is often said, "As the slope goes, so goes the It is often said, "As the slope goes, so goes the velocity." velocity."

Whatever characteristics the velocity has, the slope Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa). will exhibit the same (and vice versa).


What can you tell me about each objects What can you tell me about each objects velocity?velocity?

Object 1 has a constant Object 1 has a constant

positive velocity.positive velocity. Object 2 has no velocity.Object 2 has no velocity. Object 3 has a constant Object 3 has a constant

negative velocity.negative velocity.


Instantaneous velocity – velocity at a specific Instantaneous velocity – velocity at a specific point in timepoint in time

Can be found by the tangent of a curve. Can be found by the tangent of a curve.


What do these graphs tell you about the What do these graphs tell you about the velocity?velocity?

Slow, Rightward(+)Constant VelocitySlow, Rightward(+)Constant Velocity Fast, Rightward(+)Constant VelocityFast, Rightward(+)Constant Velocity


What do these graphs tell you about the What do these graphs tell you about the velocity?velocity?

Slow, Leftward(-)Constant VelocitySlow, Leftward(-)Constant Velocity Fast, Leftward(-)Constant VelocityFast, Leftward(-)Constant Velocity


What do these graphs tell you?What do these graphs tell you?

Negative (-) Velocity, Slow to FastNegative (-) Velocity, Slow to Fast Negative (-) Velocity, Fast to SlowNegative (-) Velocity, Fast to Slow How would you make this positive?How would you make this positive?

PracticePractice The following graph represents the motion of a The following graph represents the motion of a

car. What can you tell me about the carcar. What can you tell me about the car’’s s motion based on the graph?motion based on the graph?

The car has a rightward velocity. The car has a The car has a rightward velocity. The car has a changing velocity. The car is moving from changing velocity. The car is moving from slow to fast since the slope changes from small slow to fast since the slope changes from small big.big.

PracticePractice The following graph represents the motion of a The following graph represents the motion of a

car. What can you tell me about the carcar. What can you tell me about the car’’s s motion based on the graph?motion based on the graph?

The car has a negative velocity. The car has a The car has a negative velocity. The car has a changing velocity. The car is moving from changing velocity. The car is moving from slow to fast since the slope changes from small slow to fast since the slope changes from small to big.to big.

Four Kinematic EquationsFour Kinematic Equations


Remember:Remember: Constant acceleration - an object will change Constant acceleration - an object will change

its velocity by the its velocity by the samesame amount each second. amount each second. With this idea comes four kinematic equations.With this idea comes four kinematic equations. Δx = ½(vΔx = ½(vii + v + vff) Δt) Δt

vvff = v = vii + a Δt + a Δt

Δx = vΔx = vi i Δt + ½ a(Δt)Δt + ½ a(Δt)22

vvff2 2 = = vvii

22 + 2 a Δx + 2 a Δx


There are always 4 variablesThere are always 4 variables To use these equations you guess and check.To use these equations you guess and check. Remember to always do 4 things:Remember to always do 4 things:

1.1. Draw a diagramDraw a diagram

2.2. Write what you knowWrite what you know

3.3. Write what you needWrite what you need

4.4. Guess and checkGuess and check LetLet’’s practice…s practice…

Four Kinematic EquationsFour Kinematic Equations Ima Hurryin is approaching a stoplight moving Ima Hurryin is approaching a stoplight moving

with a velocity of +30.0 m/s. The light turns with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/sstop. If Ima's acceleration is -8.00 m/s22. What is . What is the displacement of the car during the skidding the displacement of the car during the skidding process. process.

DiagramDiagram Knowns?Knowns? Unknowns?Unknowns? EquationEquation


Ben Rushin is is waiting at a stoplight. When it Ben Rushin is is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a finally turns green, Ben accelerated from rest at a rate of a 6.00 m/srate of a 6.00 m/s2 2 for a time of 4.10 seconds. for a time of 4.10 seconds. Determine the displacement of Ben's car during Determine the displacement of Ben's car during this time period.this time period.



A racing car reaches a speed of 42m/s. It then A racing car reaches a speed of 42m/s. It then begins a uniform negative acceleration, using its begins a uniform negative acceleration, using its parachute and brakes and comes to rest 3.5s later. parachute and brakes and comes to rest 3.5s later. What is the distance that it takes the car to stop. What is the distance that it takes the car to stop.



A plane starting at rest at one end of a runway A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8m/sundergoes a uniform acceleration of 4.8m/s22 for for 15s before takeoff. What is its speed at takeoff?15s before takeoff. What is its speed at takeoff?


In a speed boat race the time starts when the In a speed boat race the time starts when the boat has a speed of 5m/s. It accelerates at a boat has a speed of 5m/s. It accelerates at a constant rate of 3.3m/sconstant rate of 3.3m/s22, with a final velocity , with a final velocity of 45m/s. How far was the race?of 45m/s. How far was the race?

Practice makes ….Practice makes ….

Try theseTry these

pg 53# 1-2, pg 55# 1-2, pg 58#1-3pg 53# 1-2, pg 55# 1-2, pg 58#1-3

Free Fall!!!!Free Fall!!!!(show video)(show video)

Free Fall!!!!Free Fall!!!!

Free FallFree Fall

IIs when an object is falling under the sole s when an object is falling under the sole influence of gravityinfluence of gravity

Two important facts:Two important facts: Free falling objects do Free falling objects do notnot encounter air encounter air

resistance (in this class)resistance (in this class) Free fall is a downward acceleration toward Free fall is a downward acceleration toward

earth (the sign gets tricky)earth (the sign gets tricky)

Free FallFree Fall

formally known as formally known as ““acceleration of gravitacceleration of gravityy”” = g = g

g = 9.81m/sg = 9.81m/s22

Often times estimated at 10m/sOften times estimated at 10m/s22 or 9.8m/s or 9.8m/s22

There are slight variations that are affected There are slight variations that are affected by altitude, we will ignore this. by altitude, we will ignore this.

Free FallFree Fall

g is independent of 3 things:g is independent of 3 things: time ittime it’’s been fallings been falling mass of the objectmass of the object if it started at rest or notif it started at rest or not

A deeper lookA deeper look

Think of it this way:Think of it this way:

Δv = 9.8 m/sΔv = 9.8 m/s Δt = 1s Δt = 1s This means every 1s the velocity This means every 1s the velocity

increases 9.8m/sincreases 9.8m/s

t

va


Think of it this way:Think of it this way:

So how fast would you be going 3 So how fast would you be going 3 seconds after jumping out an airplane?seconds after jumping out an airplane?

How about 5 min?How about 5 min? Terminal Velocity – speed Terminal Velocity – speed when the when the

force of air resistance is equal and force of air resistance is equal and opposite to the force of gravity.opposite to the force of gravity.

(around 55m/s for humans)(around 55m/s for humans)

t

va


Δv = 9.8 m/sΔv = 9.8 m/s Δt = 1s Δt = 1s This means every 1s This means every 1s

the velocity increases the velocity increases 9.8m/s9.8m/s

Time (s) Velocity

1 9.8m/s

2 19.6m/s

3 29.4m/s

4 39.2m/s

5 49.0m/s

Working BackwardsWorking Backwards

It all works backward as well. It all works backward as well. If a ball is thrown straight up:If a ball is thrown straight up:

It will decelerate at 9.81m/sIt will decelerate at 9.81m/s22

At the top of itAt the top of it’’s path the ball s path the ball ““hangshangs”” in in mid air.mid air.

At bottom of itAt bottom of it’’s path the balls velocity is s path the balls velocity is equal to vequal to vii

See Diagram….See Diagram….


A worker drops a wrench from the top of a A worker drops a wrench from the top of a tower 80m tall. What is the velocity when the tower 80m tall. What is the velocity when the wrench strikes the ground?wrench strikes the ground?



Jason hits a volleyball so that it moves with and Jason hits a volleyball so that it moves with and initial velocity of 6m/s straight upward. If the initial velocity of 6m/s straight upward. If the volleyball start 2m above the floor. How long volleyball start 2m above the floor. How long will it be in the air before it strikes the floor?will it be in the air before it strikes the floor?



A ball is thrown straight up into the air at an A ball is thrown straight up into the air at an initial velocity of 25m/s. How long does it take initial velocity of 25m/s. How long does it take for it to reach the top of its path? How far up for it to reach the top of its path? How far up does it travel?does it travel?



Try theseTry these

pg 64 Practice F # 1-4pg 64 Practice F # 1-4


HomeworkHomework

pg 59 # 1-3, 5-6pg 59 # 1-3, 5-6

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Fill in the missing bubble…. Kinematics in One Dimension Chapter 2