Unit 2 Linear MotionUnit 2 Linear Motion

I. Outline

A. Motion defined1. Position vs. Time

B. Linear MotionC. Graphing Linear MotionD. SpeedE. DistanceF. DisplacementG. VelocityH. Acceleration

A. What is Relative Motion?A. What is Relative Motion?

A. Motion DefinedA. Motion Defined

1.1. Does everything move? How would Does everything move? How would explain a car moving?explain a car moving?

2.2. If you place a book on your desk, is If you place a book on your desk, is it in motion?it in motion?

3.3. Is motion relative?Is motion relative?

4.4. Yes, but Yes, but relativerelative to WHAT? . to WHAT? .

4.4. The earth is moving around the sun, The earth is moving around the sun, therefore, the book is moving relative to therefore, the book is moving relative to the sunthe sun

5.5. The car is moving relative to the road or The car is moving relative to the road or tracktrack

6.6. The space shuttle is moving relative to The space shuttle is moving relative to the Earth below.the Earth below.

7.7. What do these two objects have in What do these two objects have in common?common?

8. Distance from a reference point and time

1. Position vs. Time

a) Position location relative to a fixed reference point

i. Why a fixed reference point?ii. farmer plowing furrows or a dancer

Tells the kid to focus on a object on other side of field and not get distracted

When finished lines all over. Why? What is wrong with this picture?

Kid responds, “Cow kept moving.” Distance from a fixed point, a point that is not

moving

B. What is Linear Motion?B. What is Linear Motion?

1.1. Motion means the Motion means the raterate at which at which something happens. E.g. How fast something happens. E.g. How fast your car travels down the freeway…your car travels down the freeway…or this bird!or this bird!

2.2. Three components of Three components of rate:rate:a)a) SpeedSpeed

b)b) VelocityVelocity

c)c) AccelerationAcceleration

How do you know that the bird is moving and NOT just doing the “moonwalk”Why can’t you tell you are doing 400 mph in an airplane?

4.4. Simplest form of Simplest form of motion-moving along a motion-moving along a straight line or path.straight line or path.

5.5. Horizontal or vertical but always a Horizontal or vertical but always a straight pathstraight path

6.6. Position Position relativerelative to what?to what? Movement relative to a motionless pointMovement relative to a motionless point

Earth…..Earth….. Sun……Sun…… Earth is spinning about 1000 mph or 460 meters Earth is spinning about 1000 mph or 460 meters

per second-per second- - what happens if the earth stops - what happens if the earth stops spinning??? spinning???

Splat!-you are the bug on the windshield!Splat!-you are the bug on the windshield!

C. Graphing Linear Motion

1. y=mx+b or slope for a linear fit. 2. You will be making graphs!!!! 3. X and Y coordinates

D. SpeedD. Speed

1.1. SpeedSpeeda)a) Is the measure of Is the measure of

how how fast (the rate) fast (the rate) something is something is movingmoving

b)b) Distance/timeDistance/time e.g. e.g. kilometer per hour kilometer per hour or (km/h) coveredor (km/h) covered

c)c) 50 mph or 30 km/h50 mph or 30 km/h

d)d) DistanceDistance = = milesmilese)e) Time hourTime hour

2.2. Instantaneous Speed:Instantaneous Speed:a)a) The The speed at any given instantspeed at any given instantb)b) E.g. Cars accelerate and decelerate all the time E.g. Cars accelerate and decelerate all the time

while driving-stop light speed is 0 km/h, on the while driving-stop light speed is 0 km/h, on the Autobahn a car may travel up to 130 km/h Autobahn a car may travel up to 130 km/h

3.3. Average SpeedAverage Speed: : ( must be ( must be betweenbetween largest & smallest largest & smallest numbers)numbers)

a)a) How fast a car will travel over entire distance How fast a car will travel over entire distance E.g. tripE.g. trip

b)b) Average speed = total distance/ total time Average speed = total distance/ total time intervalinterval

c)c) Ave. sp. 60 km/h if you traveled 240 km/4 hAve. sp. 60 km/h if you traveled 240 km/4 h

4. What is the speedometer on your car registering?

5. What is the tachometer on your car registering?

How would you calculate average How would you calculate average speed???speed???

Practice QuestionsPractice Questions

1.1. If the odometer reads 0 at the If the odometer reads 0 at the beginning of a trip and beginning of a trip and 35 35 kmkm a half a half hour laterhour later(.5-hr(.5-hr),), what is the average what is the average speed?speed?

2.2. Would it be possible to attain this Would it be possible to attain this average speed and average speed and never never exceed a exceed a reading of 70km/h on the reading of 70km/h on the speedometer?speedometer? d

s t

AnswersAnswers

1.1. 35 km/0.5 h = 70 km/h 35 km/0.5 h = 70 km/h a)a) Average speed=total distance/time Average speed=total distance/time

interval (or m/s)interval (or m/s)

2.2. No,No, not if the trip started at rest. not if the trip started at rest. instantaneous speed less than 70 instantaneous speed less than 70 km/h would have to be km/h would have to be compensated with speeds greater compensated with speeds greater than 70 km/hthan 70 km/h

E. How would you find E. How would you find distance???distance???

1.1. Distance Distance = average speed X time= average speed X time

2.2. 70 km 70 km = 35 km/h x 2 hr (km/h x = 35 km/h x 2 hr (km/h x 2hr/1 hours cancel out) 35 k2hr/1 hours cancel out) 35 kmm xx 2h

3.3. h 1h 1

Dist (m)

Speed (m/s)

Time (s)

S = d t

Practice questionsPractice questions

1.1. If a cheetah can maintain a If a cheetah can maintain a constant speedconstant speed of of 25m/s25m/s, it will , it will cover 25 meters every second. At cover 25 meters every second. At this rate, how far will it travel in this rate, how far will it travel in 10 10 secondsseconds? In ? In 1 minute1 minute??

d

s t

Answer=Distance = average speed Answer=Distance = average speed x the time intervalx the time interval

1.1. 25 m/s X 10 s = 25 m/s X 10 s = a)a) 250m250m

2.2. 25 m/s X 60 s =25 m/s X 60 s =a)a) 1500m1500m

Bowing Ball Velocity lab…and Bowing Ball Velocity lab…and distance too?distance too?

Time to play!Time to play! Speed lab and or bowling ball Speed lab and or bowling ball

velocityvelocity

F. One more thing…DisplacementF. One more thing…Displacement

1.1. Displacement vs. Displacement vs. distancedistance

a)a) DisplacementDisplacement isis

b)b) shortest distance shortest distance traveled between all traveled between all the pointsthe pointsa)a) ““as the crow flies”as the crow flies”

c)c) Distance Distance is total is total distance traveleddistance traveled Driving distanceDriving distance

Distance vs. DisplacementDave leaves his house to go to school. He drives to Leon’s house to get Leon.

Dave’s House

Leon’s house

Then he drives to Jenna’s house to pickup Jenna.Then they all go to school.

What is Dave’s net displacement?

What distance has Dave traveled?

Distance and Displacement Defined

1. Distance = total amount of “ground covered” during a given time interval.

a) E.g. a runner is at the 50 m mark at 1 s.

2. Displacement = straight-line distance in a given direction from the starting point to the ending point for a given time interval.

a) E.g. straight line from starting position DHS to ST George for ending position.

Time to Play! Displacement Lab

1. You will walk this out and measure with a meter stick. We will do the same lab again when we get to vectors and THEN we will add the math. GOT IT?

2. Demo with motion sensor, track, and car

G. VelocityG. Velocity

1.1. Speed Speed in given directionin given direction e.g. 50 e.g. 50 mp/h horizontal or vertical. mp/h horizontal or vertical.

2.2. Velocity is Velocity is how fasthow fast andand whatwhat directiondirection “it” is moving e.g. car, “it” is moving e.g. car, boat, plane etc.boat, plane etc.

3.3. Constant vs. changing velocityConstant vs. changing velocitya)a) ConstantConstant=speed and direction are the =speed and direction are the

samesame

b)b) It isIt is impossibleimpossible to detect motion at to detect motion at constant speed.constant speed.

c)c) In a car you detect acceleration and In a car you detect acceleration and negative acceleration (deceleration)negative acceleration (deceleration)

d)d) ChangingChanging=one or both are changing =one or both are changing e.g. acceleratinge.g. accelerating

Question Question

The speedometer of a car moving The speedometer of a car moving northwardnorthward reads 60 km/h. It passes reads 60 km/h. It passes another car that travels another car that travels southwardsouthward at at 60 km/h. Do both cars have the60 km/h. Do both cars have the same same speed, velocity?speed, velocity?

AnswerAnswer

Same speed = yes both 60km/hSame speed = yes both 60km/h Same velocity = no, one northward, Same velocity = no, one northward,

other southwardother southward

e. Velocity Equatione. Velocity Equation

1.1. Average velocity= change in Average velocity= change in distance/change in time, it is a distance/change in time, it is a ratio!ratio!

2.2. Velocity means m/s Velocity means m/s i.i. v = ∆d / ∆t v = ∆d / ∆t

ii.ii. ∆∆d = dd = d1 or f1 or f – d – d00

iii.iii. ∆∆t = tt = t1 or f1 or f – t – t00

iv.iv. To give us meters per secondTo give us meters per second

2. In physics average velocity involves: Position (usually in meters)Position (usually in meters) Time (seconds) Time (seconds) Hence velocity is m/sHence velocity is m/s

3.3. It is the It is the change in positionchange in position divided by divided by the the time intervaltime interval during which that during which that change took placechange took place

Displacement Average Velocity

4. The average velocity equation rearranged

a)a) v = ∆d / ∆tv = ∆d / ∆tb)b) Times each side by ∆tTimes each side by ∆tc)c) v ∆t = ∆d v ∆t = ∆d

d)d) v ∆t = dv ∆t = d1 1 – d– d00

e)e) Add Add + +dd0 0 to each side to cancel out the to each side to cancel out the minusminus

f)f) dd00 + v ∆t = d + v ∆t = d11

Velocity Questions

5. A bike travels at a constant speed of 4.0 m/s for 5 s. How far does it go?

a) Intuitively we know it is 4.0 m/s x 5 s = 20mb) Using our equation

i.i. v = ∆d / ∆tv = ∆d / ∆t

ii.ii. Times each side by ∆tTimes each side by ∆t

iii.iii. v∆t = ∆d v∆t = ∆d

iv.iv. v∆t = dv∆t = d1 1 – d– d00

v.v. Add Add + +dd0 0 to each side to cancel out the minusto each side to cancel out the minus

vi.vi. dd00 + v∆t = d + v∆t = d11

V = 4.0 m/s and is constant so no V = 4.0 m/s and is constant so no changechange

∆∆t = tt = t11 – t – t0, 0, which is 5.0 s – 0 s =5 swhich is 5.0 s – 0 s =5 s dd0 0 = 0= 0 Therefore: dTherefore: d00 + v∆t = d + v∆t = d11

0 = (4.0 m/s) (5.0 s) = 20 meters0 = (4.0 m/s) (5.0 s) = 20 meters

A bike accelerates from 0.0 m/s to 4.0 m/s in 4.0 s. What distance does it travel?

dd00 + v∆t = d + v∆t = d11

0 + (4.0 m/s) (4 s) = 16 m0 + (4.0 m/s) (4 s) = 16 m

H. AccelerationH. Acceleration

1.1. Acceleration is Acceleration is the ratethe rate at which the at which the velocity is changingvelocity is changing……

2.2. Formula Formula = acceleration =change of = acceleration =change of speed/time intervalspeed/time interval

3.3. Speed and velocity are Speed and velocity are measured in measured in units of distance per time d/tunits of distance per time d/t (distance and time)(distance and time)

4. Acceleration equation: a= ∆v/∆t = v1- v0/t1- t0

Acceleration…Question (concept)Acceleration…Question (concept)

5.5. Suppose a car moving in a straight Suppose a car moving in a straight line steadily increases its speed line steadily increases its speed each second, first from 35 to each second, first from 35 to 40/km/h, then form 40 to 45 km/h, 40/km/h, then form 40 to 45 km/h, then from 45 to 50 km/h. What is its then from 45 to 50 km/h. What is its acceleration?acceleration?

a)a) The speed increased by 5 km/h The speed increased by 5 km/h during each 1 second interval, thus, during each 1 second interval, thus, acceleration is 5 km/h during each acceleration is 5 km/h during each interval….interval….

b)b) help!help!

c)c) We are now into accelerationWe are now into acceleration

6.6. AccelerationAcceleration is the rate at which is the rate at which velocity is changing with respect to velocity is changing with respect to time! time!

e.g. you want to beat your friend to e.g. you want to beat your friend to Atlantis Burger so you speed up and pass Atlantis Burger so you speed up and pass him on the frontage road!him on the frontage road!

7.7. Acceleration = Acceleration = change of velocitychange of velocity / / time intervaltime interval

ISIS negative acceleration real?negative acceleration real? YES!YES!

Acceleration Question Acceleration Question

8.8. In 5 seconds a car moving in a In 5 seconds a car moving in a straight line increases its speed straight line increases its speed from 50 km/h to 65 km/h, while a from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a truck goes from rest to 15 km/h in a straight line. straight line.

9.9. Which undergoes greater Which undergoes greater acceleration?acceleration?

10.10. What is the acceleration of each What is the acceleration of each vehicle?vehicle?

AnswerAnswer

11.11. Acceleration = change in Acceleration = change in speed/time intervalspeed/time interval

a)a) 15 km/h/5s = 3km/h/s15 km/h/5s = 3km/h/s

b)b) Both are equal acceleration, Both are equal acceleration,

c)c) rates of change the samerates of change the same

d)d) Even thought speeds involved are Even thought speeds involved are quite differentquite different

e)e) VV11 – v – v00/ 5s (time between 2 points)/ 5s (time between 2 points)

Time to play…graph matching

I. Summary: Rate of Change of Motion1. The rate of change of distance with

respect to time is speed. Pos. vs. time

2. The rate of change of displacement with respect to time is velocity.

m/s vs. time to find a distance

3. The rate of change of velocity is acceleration.

m/s vs. time to find a rate

Questions

Chapter 2 from conceptual physics book (blue book)

questions 1-14, 26-30 Questions from chapter five, the red

physics book pg 97Chapter 5 questions and problems pg. 97: 17, 18, 23-28, 29 (calculator problem) 30, Pg 110: 33, 35 (no calculator manually make graph) 38, 40, and even problems 44, 46, 50, 54a, 58a

B. Free Fall

1. Free fall a) (one-dimensional) b) motion of any object

under the influence of gravity only

c) no air resistance or friction effects of any kinda) We are not going

to do calculations involving air resistance

d) If you jump off a chair, you are in free fall.

2. Galileo discovered (minus air resistance) freely falling objects had the same acceleration.

3. He also discovered that the object, regardless of shape, size, height from which the object was dropped, thrown or even the mass acceleration was the same for all falling objects

1. Paper and baseball demo2. After Galileo Isacc Newton proved Galileo’s theory

4. Conclusion: magnitude of acceleration is denoted by the symbol:

g = 9.81 m/s2

4. Review one dimension motiona) Orange sheet review b) For free fall use the same formulas as beforec) Now acceleration is g (9.80 m/s2 )

Acceleration is known due to gravity Key words:

Dropped = 0 initial velocity Tossed = non zero initial velocity Fall or free fall = acceleration is g Velocity when object hits the ground = velocity at last

instant before contact with ground is made

Time to play Pascal lab with free fall

Free Fall problems Chap. 5 questions Pg 106

31-33 Pg 113

66-70, 73 and 74

formulasformulas

v = gt v = gt v = instantaneous speedv = instantaneous speed g = acceleration ( 9.8 m/sg = acceleration ( 9.8 m/s22 ) force of ) force of

gravitygravity t = timet = time Sometimes v=at (a is same as g)Sometimes v=at (a is same as g)

formulasformulas

d = d = ½½ gt gt22

d = distance object falls on the y axisd = distance object falls on the y axis g = acceleration ( 9.8 m/sg = acceleration ( 9.8 m/s22 ) force of ) force of

gravitygravity tt22 = time squared = time squared ½ (.5) x ½ (.5) x gtgt22

problemproblem

What would be the velocity of a What would be the velocity of a falling rock starting from rest, 4s, 8s falling rock starting from rest, 4s, 8s and 15s?and 15s?

v = (10 m/sv = (10 m/s2 2 ) (0s) = 0m/s ) (0s) = 0m/s V = (10 m/sV = (10 m/s22 )(4s) = 40m/s )(4s) = 40m/s 80m/s and 150m/s80m/s and 150m/s Position and timePosition and time

problemsproblems

Find the speed required to throw a ball Find the speed required to throw a ball straight up and have it return straight up and have it return 6s 6s later. later. Neglect air resistance.Neglect air resistance.

Hint: v up = v down (3s + 3s) = 6sHint: v up = v down (3s + 3s) = 6s What is the velocity?What is the velocity? Now solve for distance…..Now solve for distance….. d = d = ½½ gt gt22

Why ½? Why ½? 3 seconds up and 3s seconds down3 seconds up and 3s seconds down

Table pg 17 and 20Table pg 17 and 20

TimeTime Speed/Speed/velocityvelocity

distancedistance

0s0s 0ms0ms 0m0m

1s1s 10m/s10m/s 5m5m

2s2s 20m/s20m/s 20m20m

3s3s 30m/s30m/s 45m45m

4s4s 40m/s40m/s 80m80m

5s5s 50m/s50m/s 125m125m

tt gtgt ½ gt½ gt22

Time to play!!!Time to play!!!

Free fall labFree fall lab