Linear MotionLinear Motion

Or 1 Dimensional KinematicsOr 1 Dimensional Kinematics

This problem was missed a lot This problem was missed a lot of 1314 benchmark. Did not of 1314 benchmark. Did not put in signs for calculationput in signs for calculation

A car is traveling west and A car is traveling west and decreases its speed from 30 m/s decreases its speed from 30 m/s to 23 m/s in 2 seconds. What is to 23 m/s in 2 seconds. What is the car’s average acceleration? the car’s average acceleration? Include direction.Include direction.

9/99/9 Goal: Begin Motion Goal: Begin Motion Pick up Sample WS & calculator. Pick up Sample WS & calculator. Turn in Bubble Gum Lab to Sorter Turn in Bubble Gum Lab to Sorter If you were absent, pick up the Bubble If you were absent, pick up the Bubble

Gum Lab from the mailbox. It will be Gum Lab from the mailbox. It will be due Thursday.due Thursday.

Tests are will be graded by tomorrow.Tests are will be graded by tomorrow. Solve Now in dim. Analysis format:Solve Now in dim. Analysis format: A starship travels at 6.5 x 108 m/sec.

How far does it travel in one day?

9/10 If absent Tue, get Sample WS 9/10 If absent Tue, get Sample WS II

Goal: Calculate practice: distance, Goal: Calculate practice: distance, displacement, speed and velocitydisplacement, speed and velocity

Tests are graded. Missing: Taylor Tests are graded. Missing: Taylor Morgan,, Rina Rraci, Katana Shoemake, Morgan,, Rina Rraci, Katana Shoemake, Alexis Baldwin, Morgan Barrentine Alexis Baldwin, Morgan Barrentine

Solve Now:Solve Now: Thomas starts in a maze. He runs east Thomas starts in a maze. He runs east

for 10 m and hits a dead end. He then for 10 m and hits a dead end. He then turns around and runs west for 15 m. turns around and runs west for 15 m. What distance did he run? What is his What distance did he run? What is his displacement from his origin? Did he displacement from his origin? Did he run into any Grievers?run into any Grievers?

9/119/11 Have Linear Motion WS out to be checkedHave Linear Motion WS out to be checked Pick up Acceleration WS and a calculatorPick up Acceleration WS and a calculator Grades to date have been put in. There are quite a Grades to date have been put in. There are quite a

few zeros few zeros It is your responsibility to check It is your responsibility to check gradebook.gradebook.

This was what was turned in last weekThis was what was turned in last week– Dim Analys WS (10 problems) due 9/2Dim Analys WS (10 problems) due 9/2– Tue 9/5 Sci Not practice due 9/2Tue 9/5 Sci Not practice due 9/2– Safety Review due 9/4Safety Review due 9/4– Sci Method Station due 9/5Sci Method Station due 9/5– Bubble gum Lab due 9/8Bubble gum Lab due 9/8– THIS WEEK ONLY, I will accept any of these THIS WEEK ONLY, I will accept any of these

assignments today since I was out of town last assignments today since I was out of town last week.week.

RetestsRetests

Scored below 70 on original testScored below 70 on original test Must come in and perform test Must come in and perform test

corrections before or after schoolcorrections before or after school Retests only after schoolRetests only after school You must sign up at least one day in You must sign up at least one day in

advance for a retake. You may not advance for a retake. You may not do a retake if you have not done test do a retake if you have not done test corrections. corrections.

How long does it take a motorcycle , How long does it take a motorcycle , initially at rest to increase its speed initially at rest to increase its speed to 15 m/s if it accelerates at to 15 m/s if it accelerates at 0.95m/s0.95m/s22??

How many centigrams in a gram?How many centigrams in a gram? How many meters in a kilometer?How many meters in a kilometer?

Linear MotionLinear Motion

Great Website for Linear Motion

http://www.glenbrook.k12.il.us/gbssci/phys/class/1DKin/U1L1a.html

Kinematics in one dimensionKinematics in one dimension the study of linear motion (in a the study of linear motion (in a

straight line -not curved) straight line -not curved)

MotionMotion

What does it mean for an object What does it mean for an object to be in motion?to be in motion?

It is the change in position of an It is the change in position of an object as compared to a object as compared to a reference pointreference point

*

Is the brick wall moving?Is the brick wall moving?

Not from where she’s sitting, but…Not from where she’s sitting, but…

……from space, the earth rotates from space, the earth rotates and the wall with it.and the wall with it.

So, whether or not something is moving depends on your frame of reference. *

Frame of ReferenceFrame of Reference a fixed point used to determine a fixed point used to determine

magnitude and direction of motionmagnitude and direction of motion Magnitude?Magnitude? See Video HereSee Video Here

RateRate a change in a given quantity over a a change in a given quantity over a

specified period of time (examples: specified period of time (examples: velocity and acceleration)velocity and acceleration)

What are some units of What are some units of measurement?measurement?

Scalar quantityScalar quantity a measurementa measurement Magnitude Magnitude No direction impliedNo direction implied Ex. mass, volume, density, distance, Ex. mass, volume, density, distance,

speedspeed

Vector quantityVector quantity a measurementa measurement MagnitudeMagnitude DirectionDirection Ex.: displacement, velocity, Ex.: displacement, velocity,

acceleration, forceacceleration, force

DistanceDistance the length of the actual path taken the length of the actual path taken

by the object regardless of directionby the object regardless of direction scalar quantityscalar quantity SI units include m, kmSI units include m, km

DisplacementDisplacement length (measured in a straight line) length (measured in a straight line)

from the reference point to the from the reference point to the object (implies a given direction)object (implies a given direction)

Sometimes on graph labeled as Sometimes on graph labeled as PositionPosition

vector quantityvector quantity SI units include m, kmSI units include m, km

SpeedSpeed change in distance divided by change in change in distance divided by change in

time time s =d/t or v =d/t s =d/t or v =d/t s is typically written “v”s is typically written “v” Where Where

– s = speed s = speed – d = distanced = distance– t = timet = time

scalar quantityscalar quantity SI units include m/sec or cm/sec.SI units include m/sec or cm/sec.

VelocityVelocity speed in a given direction speed in a given direction magnitude and direction included in magnitude and direction included in

the measurementthe measurement vector quantityvector quantity SI units include m/sec or cm/sec.SI units include m/sec or cm/sec. (v = ∆d/∆t) where(v = ∆d/∆t) where

∆∆d= change in displacement (dd= change in displacement (dfinalfinal-d-dinitialinitial))

∆∆t= change in time (tt= change in time (tfinalfinal-t-tinitialinitial))

What is the unit for:What is the unit for:

Speed?Speed? m/sm/s Velocity?Velocity? m/sm/s Acceleration?Acceleration? m/sm/s22

What is the displacement for What is the displacement for Bob the Bear?Bob the Bear?

d = df – di

d = 90m – 20m = 70m

Displacement is not always equal to Displacement is not always equal to distance travelled! What is Clyde the distance travelled! What is Clyde the

Caterpillar’s displacement?Caterpillar’s displacement?

d = df – di

d = 80m – 20m = 60m

Sign for VectorsSign for Vectors

the sign indicates directionthe sign indicates directioncan be positive or negativecan be positive or negativeRight , East , or North are +Right , East , or North are +Left, West, or South are -Left, West, or South are -

What is the displacement for What is the displacement for Frank the Fish?Frank the Fish?

-70mThe negative sign tells us he is moving opposite the direction of the number line—in this case, to the left.

Ex 1Ex 1 Travis needs his physics notes. He

walks from his house 8 yards due east towards Shannon’s house to borrow her notes. At this point Travis realizes he left his phone at home and runs back to get it. After picking up his phone he continues the 14 yards east to Shannon’s house. What was the distance and displacement?

EX 1 Travis needs his physics notes. He walks from his house 8 yards due east towards Shannon’s house to borrow her notes. At this point Travis realizes he left his phone at home and runs back to get it. After picking up his phone he continues the 14 yards east to Shannon’s house. What was the distance and displacement?

Distance = 8yds + 8yds + 14 yds = 30 ydsDistance = 8yds + 8yds + 14 yds = 30 yds

Displacement = Displacement = ++8yds + 8yds + --8yds + 8yds + ++14 yds = 14 yds = ++14 yds or 14 yds East14 yds or 14 yds East

Average VelocityAverage Velocity The average velocity of an object is The average velocity of an object is

defined as the displacement of an defined as the displacement of an object divided by the time in which it object divided by the time in which it took place.took place.

Average velocity = Average velocity =

vvavgavg = = d = = d22-d-d11

tt2-2-tt11

Change in position

Change in timedt

**

Ex 2Ex 2

A racing car driven by Speed E. Demon travels 480 kilometers in 2.0 hours. Calculate the average speed in km/hr and convert to m/s.

Ex 2 A racing car driven by Speed E. Demon travels 480 kilometers in 2.0 hours. Calculate the average speed in km/hr and convert to m/s.

Step 3Show substitution (with units) and answerv = 480 km= 480 km= 240 km/hr240 km/hr

2 hrs2 hrs

Step 1List Variablesd= 480 kmv = ?t = 2 hrs

Step 2Show Formula (arranged to solve for unknown)v = d t

Step 4 This problem requires dimensional analysis240km 1000m 1hr = 33.33 m/s2 hr 1 km 3600s

Ex. 3Ex. 3Sunday Driver takes her CadillacSunday Driver takes her Cadillacfor a spin and travels 50.0 km for a spin and travels 50.0 km at an average speed of 35.0 m/s. at an average speed of 35.0 m/s. How longHow long (in seconds) was she (in seconds) was she driving her car?driving her car?

1428.57 sec1428.57 secRemember to change km to m!Remember to change km to m!t = d/v NOT dvt = d/v NOT dv

Sample 4Sample 4

A car travels at a constant speed of 4m/s for 5s. How far does it go in m?

d = vt20 m

Skip this year

A car travels at 60 km/hr for 200 km. It then speeds up to 90km/hr and travels an additional 200 km. What is its average velocity?

AccelerationAcceleration change in velocity divided by change change in velocity divided by change

in time (a = ∆v/∆t)in time (a = ∆v/∆t) WhereWhere

∆∆v = (vv = (vfinalfinal-v-vinitialinitial))

∆∆t =(tt =(tfinalfinal-t-tinitialinitial))

vector quantityvector quantity SI units include m/secSI units include m/sec22 or cm/sec or cm/sec22

AccelerationAcceleration

Mathematically,Mathematically,

Avg acceleration = Avg acceleration =

aaavgavg = = = = = =

Change in velocityChange in time

vt

vf - vi

tf - ti

**

vf - vi

t

Ex 1Ex 1

A rocket takes off from rest from the launching pad. It accelerates to a speed of 150m/s during a time period of 10 seconds. What was the acceleration experienced by the rocket?

Ex 1 Ex 1 A rocket takes off from rest from the launching pad. It accelerates to a speed of 150m/s during a time period of 10 seconds. What was the acceleration experienced by the rocket?

Step 3Show substitution (with units) and answer

a = 150 m/s - 0m/s = 150 m/s - 0m/s = 15 m/s15 m/s22

10 sec10 sec

Step 1List Variablesd= vi = 0m/s (at rest)vf = 150 m/sa= ?t = 10 sec

Step 2Show Formula (rearranged)a = vf – vi

t

Ex 2Ex 2

Suppose a treadmill has an average acceleration of 4.7 m/s2. If the treadmill starts at 1.7m/s, what would its velocity be after 150 seconds?

Ex 2 Ex 2 Suppose a treadmill has an average acceleration of 4.7 m/s2. If the treadmill starts at 1.7m/s, what would its velocity be after 150 seconds?

Step 3Show substitution (with units) and answer

vvff = 1.7m/s + [(1.7m/s + [(4.7 m/s2)(150 sec)150 sec)

vvff = 706.7 m/s = 706.7 m/s

Step 1List Variablesd= vi = 1.7 m/s vf = ?a= 4.7 m/s2

t = 150 sec

Step 2Show Formula (rearranged)vf = vi + at

9/12 Get a calculator and blue 9/12 Get a calculator and blue formula chart (by calculators). Solve formula chart (by calculators). Solve

this now: Practice Problem Athis now: Practice Problem A

What would the acceleration What would the acceleration of a car be if it goes from of a car be if it goes from 100.0 m/s to 80.0 m/s in 5s?100.0 m/s to 80.0 m/s in 5s?

Quiz Today after warm up!

Practice Problem APractice Problem A

What would the acceleration What would the acceleration of a car be if it goes from of a car be if it goes from 100.0 m/s to 80.0 m/s in 5s?100.0 m/s to 80.0 m/s in 5s?

-4m/s2

Acceleration WS 1Acceleration WS 13. A runner takes off from rest at the starting line. He accelerates to a speed of 8.4 m/s during a time period of 3.2 seconds. What was the acceleration of the runner? 2.63 m/s2

4. A jet plane has an average acceleration of 23.8 m/s2. as it takes off from the ground. If it’s starting velocity as it leaves the ground is 29.4 m/s, what would its velocity be after 16 seconds? What would the final velocity be in km/hr? 410.2 m/s 1476.72 km/hr

5. Don’t worry about this one yet

5. A boat is sitting still. The driver starts the motor and accelerates at a constant rate until he reaches a velocity of 12.5 m/s 87 meters later. How long does it take to achieve this speed?

This is a 2 step problem.

Acceleration equationsAcceleration equations

Remember velocity, displacement, Remember velocity, displacement, and acceleration are all vector and acceleration are all vector quantities.quantities.

Indicate direction Indicate direction right or east: positive right or east: positive left or west: negativeleft or west: negative

Finish Acceleration WS I #6-8Finish Acceleration WS I #6-8

vvavgavg = Δd/ = Δd/ΔΔtt

a = Δv/a = Δv/ΔΔt = vt = vff – v – vii/t/t

a = va = vff2 2 - v- vii

22

22ΔΔdd

Δd = vΔd = viiΔΔt + ½at + ½aΔΔtt22

Δd = vΔd = viiΔΔt + t + .5.5aaΔΔtt22

a – acceleration in m/s2a – acceleration in m/s2v - change in velocity in v - change in velocity in m/sm/svf – final velocity in m/svf – final velocity in m/svi – initial velocity in m/svi – initial velocity in m/st or t – time interval in t or t – time interval in

seconds secondsd – displacement in md – displacement in m

Any of these formulas can be Any of these formulas can be rearranged!!!rearranged!!!

How do we know which formulas to How do we know which formulas to use?use?

DVVAT!!!!!DVVAT!!!!!

Example B A tricycle, initially traveling at 0.15 m/s,

experiences an acceleration of 0.045 m/s2.

What is the velocity of such tricycle after a period of 15 seconds?

Example Bvi = 0.15 m/s

a = 0.045 m/s2

t = 15 svf = ?

What equation?vvff = v = vii + a + aΔΔttvvff = = 0.15 m/s +( 0.045 m/s2)(15 s)vf = 0.83 m/s

Example CA bowling ball decelerates. If it slows

from 15.3 m/s to 2.77 m/s in 14.0 seconds, what is the measure of such deceleration?

Example Cvi = 15.3 m/s

vf = 2.77 m/s

t = 14.0 sa = ?

What equation?vvff = v = vii + a + aΔΔttSolve for aSolve for avvff = v = vii + a + aΔΔttvvff - v - vii = a = aΔΔtt(v(vff – v – vii)/)/ΔΔt = at = a

a = (2.77 m/sa = (2.77 m/s – 15.3 m/s)/(14.0 s)a= -0.895 m/s2

Example DAn arrow takes a horizontal path the

arrow slows from 26.3 m/s to 15 m/s during flight with an acceleration of

-0.83 m/s2 . How far does it travel?

Example Dvi = 26.3 m/s

vf = 15 m/s

a = -0.83 m/s2

d = ?What equation?

a=va=vff22 - v - vii

22 / 2 / 2ΔΔddSolve for dSolve for d

d=vd=vff22 - v - vii

22 / 2a / 2ad = d = (15 m/s)(15 m/s)22-(26.3-(26.3m/s)2/(2 x-0.83 m/s2)d= 281.14 m

9/12 Homework9/12 HomeworkFinish Acceleration WS I #6-8Finish Acceleration WS I #6-8

How do we refer to a change in How do we refer to a change in speed or velocity?speed or velocity?

What is acceleration?What is acceleration?

Can you have constant speed and Can you have constant speed and still be accelerating?still be accelerating?

What is the formula for acceleration?What is the formula for acceleration?

Hot Wheels TrackHot Wheels Track

A boy is spinning on a merry-go-round A boy is spinning on a merry-go-round at constant speed of 0.5 m/s. Describe at constant speed of 0.5 m/s. Describe his velocity. Describe his acceleration.his velocity. Describe his acceleration.

Acceleration summaryAcceleration summary

Acceleration is change in velocityAcceleration is change in velocity Acceleration has magnitude and Acceleration has magnitude and

directiondirection If speed is constant, but the object is If speed is constant, but the object is

changing direction, there is acceleration changing direction, there is acceleration When acceleration = 0, velocity is When acceleration = 0, velocity is

constantconstant If Acceleration is – and velocity is +, the If Acceleration is – and velocity is +, the

object is slowing down.object is slowing down.

Vertical Acceleration Vertical Acceleration

Gravity in a Vacuum

This video is 3 min and 41 secondsThis video is 3 min and 41 seconds

If the link does not work, the name is If the link does not work, the name is The Mechanical Universe: The Law of Falling Bodies

Show segment Gravity in a vacuumShow segment Gravity in a vacuum

Free FallFree Fall

In the absence of air In the absence of air resistance all objects dropped resistance all objects dropped near the surface of a planet near the surface of a planet fall with the same constant fall with the same constant acceleration.acceleration.

Free fall accelerationFree fall accelerationAlso called acceleration due to Also called acceleration due to

gravitygravitydenoted with the symbol denoted with the symbol gg..g = 9.8m/sg = 9.8m/s22,, since it is natural to fall down, since it is natural to fall down,

we will refer to the down we will refer to the down direction as +direction as +

g = g = aa = 9.8m/s = 9.8m/s22

Acceleration due to GravityAcceleration due to GravityWhat does it look like related to What does it look like related to

speed?speed?

If a ball was simply dropped

Freefall Practice Ex 14Freefall Practice Ex 14

Dylan sits in a tree dropping Dylan sits in a tree dropping acorns on people walking by. acorns on people walking by. If the acorns take 2.6 sec to If the acorns take 2.6 sec to hit the ground, how tall is the hit the ground, how tall is the tree in which Dylan is sitting?tree in which Dylan is sitting?

List your knowns! D-V-V-A-TList your knowns! D-V-V-A-TWhat formula will you use?What formula will you use?

d = ?d = ?

vvii = 0 m/s (0 VELOCITY BEFORE = 0 m/s (0 VELOCITY BEFORE IT DROPS!IT DROPS!

vvff

a = 9.8 m/sa = 9.8 m/s2 2 (Acceleration due to (Acceleration due to gravity)gravity)

t = 2.6 sect = 2.6 sec

What formula?What formula?d = vd = viit + .5att + .5at22

Remember since vRemember since vii=0 v=0 viit=0t=0d = .5atd = .5at22

d = (.5)(9.8d = (.5)(9.8m/sm/s22)(2.6s))(2.6s)22

d = 33.1md = 33.1m

Practice Ex15Practice Ex15

A flowerpot falls from a A flowerpot falls from a windowsill 55.0m above the windowsill 55.0m above the sidewalk below.sidewalk below.1)1) How long do the people below How long do the people below

have to move out of the way?have to move out of the way?

2)2) How fast is the flowerpot going How fast is the flowerpot going when it hits the ground?when it hits the ground?

Natalie is frustrated in Physics. Natalie is frustrated in Physics. She throws her pencil downward She throws her pencil downward with an initial velocity of .68m/s. with an initial velocity of .68m/s. Her hand is 80cm above the Her hand is 80cm above the floor. What is the velocity of the floor. What is the velocity of the pencil in m/s just before impact?pencil in m/s just before impact?

Practice Ex 16

Brent is hanging over the Brent is hanging over the bleachers at a soccer game. bleachers at a soccer game. He opens his mouth to yell at He opens his mouth to yell at someone and his gum falls someone and his gum falls out of his mouth straight out of his mouth straight down!!!! What is the velocity down!!!! What is the velocity of the gum when it strikes of the gum when it strikes the ground 15m below?the ground 15m below?

TEACHER NOTESTEACHER NOTES Describe the bet about catching a Describe the bet about catching a

dollar billdollar bill Have students measure a dollar bill Have students measure a dollar bill

in cm and convert to m (I have some in cm and convert to m (I have some cardboard ones)cardboard ones)

Meter Stick LabMeter Stick Lab

Dollar Bill?Dollar Bill? Determine length and convert to metersDetermine length and convert to meters Objective Objective Use g to determine your reaction Use g to determine your reaction

time and motor nerve conduction speedtime and motor nerve conduction speedMaterials Materials Meter StickMeter StickMethodsMethods 1. Dropping and catching the meterstick. 1. Dropping and catching the meterstick.

2. Start at zero2. Start at zero 3.Record distance of catch in centimeters3.Record distance of catch in centimeters 4. Average 5 individual trials . Convert 4. Average 5 individual trials . Convert

average to metersaverage to meters

MY DATAMY DATA

Dollar bill 15.5 cm = .155mDollar bill 15.5 cm = .155m Average of 5 catches 32.4 cm Average of 5 catches 32.4 cm

= .324 m= .324 m

Determine your reaction time (t) Determine your reaction time (t) Let aLet agg = 9.8 m/s = 9.8 m/s22

aag g simply means the acceleration due simply means the acceleration due to the force of gravityto the force of gravity Look at our velocity formulas. Do we Look at our velocity formulas. Do we have enough information to solve for have enough information to solve for time? List your D-V-V-A-T time? List your D-V-V-A-T Hint: what was the starting velocity of the Hint: what was the starting velocity of the

meterstick?meterstick?d = vd = viit + .5att + .5at2 2 what iswhat is vviit?t?d = .5atd = .5at22

Solve for tSolve for t

t = √(d/.5a)t = √(d/.5a)

Calculate timeCalculate time

What else can we figure out What else can we figure out from this data?from this data?

You know the initial velocity of the You know the initial velocity of the meter stick.meter stick.

What formula would you use to solve What formula would you use to solve for the vfor the vff??

vvff = v = vii + at + at

What goes up…What goes up…

……must come down!must come down!What happens in terms of What happens in terms of

velocity when a ball is thrown velocity when a ball is thrown into the air?into the air?

What happens in terms of What happens in terms of acceleration?acceleration?

What is your reaction time What is your reaction time related to?related to?

Determine the speed of motor neuron Determine the speed of motor neuron conduction in m/s. What 2 values do you conduction in m/s. What 2 values do you need for speed?need for speed?Assume that the impulse in the motor Assume that the impulse in the motor neuron traveled from the back of your head neuron traveled from the back of your head to the tip of your index finger. Thus, to the tip of your index finger. Thus, measure this distance to find d, make sure measure this distance to find d, make sure you record this distance in meters.you record this distance in meters.

Solve for velocity of the impulse using your Solve for velocity of the impulse using your

reaction time and distance from index reaction time and distance from index finger to back of head. finger to back of head.