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Unit 2 Linear Motion

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I. Outline A. A. Motion defined 1. 1. Position vs. Time B. B. Linear Motion C. C. Graphing Linear Motion D. D. Speed E. E. Distance F. F. Displacement G. G. Velocity H. H. Acceleration

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A. What is Relative Motion?

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A. Motion Defined 1. Does everything move? How would explain a car moving? 2. If you place a book on your desk, is it in motion? 3. Is motion relative? 4. Yes, but relative to WHAT?.

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4. The earth is moving around the sun, therefore, the book is moving relative to the sun 5. The car is moving relative to the road or track 6. The space shuttle is moving relative to the Earth below. 7. What do these two objects have in common? 8. 8. Distance from a reference point and time

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1. Position vs. Time a) a) Position location relative to a fixed reference point i. i. Why a fixed reference point? ii. 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

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B. What is Linear Motion? 1. Motion means the rate at which something happens. E.g. How fast your car travels down the freeway…or this bird! 2. Three components of rate: a) Speed b) Velocity c) Acceleration How do you know that the bird is moving and NOT just doing the moonwalk Why cant you tell you are doing 400 mph in an airplane?

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4. Simplest form of motion-moving along a straight line or path. 5. Horizontal or vertical but always a straight path 6. Position relative to what? Movement relative to a motionless point Movement relative to a motionless point Earth….. Earth….. Sun…… Sun…… Earth is spinning about 1000 mph or 460 meters per second-- what happens if the earth stops spinning??? Earth is spinning about 1000 mph or 460 meters per second- - what happens if the earth stops spinning??? Splat!-you are the bug on the windshield! Splat!-you are the bug on the windshield!

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

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D. Speed 1. Speed a) Is the measure of how fast (the rate) something is moving b) Distance/time e.g. kilometer per hour or (km/h) covered c) 50 mph or 30 km/h d) Distance = miles e) Time hour

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2. Instantaneous Speed: a) The speed at any given instant b) E.g. Cars accelerate and decelerate all the time while driving-stop light speed is 0 km/h, on the Autobahn a car may travel up to 130 km/h 3. Average Speed: ( must be between largest & smallest numbers) a) How fast a car will travel over entire distance E.g. trip b) Average speed = total distance/ total time interval c) Ave. 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?

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How would you calculate average speed???

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Practice Questions 1. If the odometer reads 0 at the beginning of a trip and 35 km a half hour later (.5- hr), what is the average speed? 2. Would it be possible to attain this average speed and never exceed a reading of 70km/h on the speedometer? d s t

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Answers 1. 35 km/0.5 h = 70 km/h a) Average speed=total distance/time interval (or m/s) 2. No, not if the trip started at rest. instantaneous speed less than 70 km/h would have to be compensated with speeds greater than 70 km/h

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E. How would you find distance??? 1. Distance = average speed X time 2. 70 km = 35 km/h x 2 hr (km/h x 2hr/1 hours cancel out) 35 k m x 2. 70 km = 35 km/h x 2 hr (km/h x 2hr/1 hours cancel out) 35 k m x 2h 3. h 1 Dist (m) Speed (m/s) Time (s) S = d t

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Practice questions 1. If a cheetah can maintain a constant speed of 25m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? In 1 minute? d s t

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Answer=Distance = average speed x the time interval 1. 25 m/s X 10 s = a) 250m 2. 25 m/s X 60 s = a) 1500m

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Bowing Ball Velocity lab…and distance too? Time to play! Time to play! Speed lab and or bowling ball velocity Speed lab and or bowling ball velocity

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F. One more thing…Displacement 1. Displacement vs. distance a) Displacement is b) shortest distance traveled between all the points a) as the crow flies c) Distance is total distance traveled Driving distance Driving distance

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Distance vs. Displacement Dave leaves his house to go to school. He drives to Leons house to get Leon. Daves House Leons house Then he drives to Jennas house to pickup Jenna. Then they all go to school. What is Daves net displacement? What distance has Dave traveled?

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Distance and Displacement Defined 1. 1. Distance = total amount of ground covered during a given time interval. a) a) E.g. a runner is at the 50 m mark at 1 s. 2. 2. Displacement = straight-line distance in a given direction from the starting point to the ending point for a given time interval. a) a) E.g. straight line from starting position DHS to ST George for ending position.

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Time to Play! Displacement Lab 1. 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. 2. Demo with motion sensor, track, and car

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G. Velocity 1. Speed in given direction e.g. 50 mp/h horizontal or vertical. 2. Velocity is how fast and what direction it is moving e.g. car, boat, plane etc.

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3. Constant vs. changing velocity a) Constant=speed and direction are the same b) It is impossible to detect motion at constant speed. c) In a car you detect acceleration and negative acceleration (deceleration) d) Changing=one or both are changing e.g. accelerating

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

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Answer Same speed = yes both 60km/h Same speed = yes both 60km/h Same velocity = no, one northward, other southward Same velocity = no, one northward, other southward

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e. Velocity Equation 1. Average velocity= change in distance/change in time, it is a ratio! 2. Velocity means m/s i. v = d / t ii. d = d 1 or f – d 0 iii. t = t 1 or f – t 0 iv. To give us meters per second

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2. 2. In physics average velocity involves: Position (usually in meters) Position (usually in meters) Time (seconds) Time (seconds) Hence velocity is m/s Hence velocity is m/s 3. It is the change in position divided by the time interval during which that change took place

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Displacement Average Velocity 4. 4. The average velocity equation rearranged a) v = d / t b) Times each side by t c) v t = d d) v t = d 1 – d 0 e) Add + d 0 to each side to cancel out the minus f) d 0 + v t = d 1

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Velocity Questions 5. 5. A bike travels at a constant speed of 4.0 m/s for 5 s. How far does it go? a) a) Intuitively we know it is 4.0 m/s x 5 s = 20m b) b) Using our equation i. v = d / t ii. Times each side by t iii. vt = d iv. vt = d 1 – d 0 v. Add + d 0 to each side to cancel out the minus vi. d 0 + vt = d 1

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V = 4.0 m/s and is constant so no change V = 4.0 m/s and is constant so no change t = t 1 – t 0, which is 5.0 s – 0 s =5 s t = t 1 – t 0, which is 5.0 s – 0 s =5 s d 0 = 0 d 0 = 0 Therefore: d 0 + vt = d 1 Therefore: d 0 + vt = d 1 0 = (4.0 m/s) (5.0 s) = 20 meters 0 = (4.0 m/s) (5.0 s) = 20 meters

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A bike accelerates from 0.0 m/s to 4.0 m/s in 4.0 s. What distance does it travel? d 0 + vt = d 1 d 0 + vt = d 1 0 + (4.0 m/s) (4 s) = 16 m 0 + (4.0 m/s) (4 s) = 16 m

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H. Acceleration 1. Acceleration is the rate at which the velocity is changing… 2. Formula = acceleration =change of speed/time interval 3. Speed and velocity are measured in units of distance per time d/t (distance and time) 4. 4. Acceleration equation: a= v/t = v 1 - v 0 /t 1 - t 0

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Acceleration…Question (concept) 5. Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40/km/h, then form 40 to 45 km/h, then from 45 to 50 km/h. What is its acceleration?

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a) The speed increased by 5 km/h during each 1 second interval, thus, acceleration is 5 km/h during each interval…. b) help! c) We are now into acceleration

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6. Acceleration is the rate at which velocity is changing with respect to time! e.g. you want to beat your friend to Atlantis Burger so you speed up and pass him on the frontage road! e.g. you want to beat your friend to Atlantis Burger so you speed up and pass him on the frontage road! 7. Acceleration = change of velocity / time interval IS negative acceleration real? IS negative acceleration real? YES! YES!

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Acceleration Question 8. In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a straight line. 9. Which undergoes greater acceleration? 10. What is the acceleration of each vehicle?

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Answer 11. Acceleration = change in speed/time interval a) 15 km/h/5s = 3km/h/s b) Both are equal acceleration, c) rates of change the same d) Even thought speeds involved are quite different e) V 1 – v 0 / 5s (time between 2 points)

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Time to play…graph matching

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I. Summary: Rate of Change of Motion 1. 1. The rate of change of distance with respect to time is speed. Pos. vs. time 2. 2. The rate of change of displacement with respect to time is velocity. m/s vs. time to find a distance 3. 3. The rate of change of velocity is acceleration. m/s vs. time to find a rate

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Questions Chapter 2 from conceptual physics book (blue book) questions 1-14, 26-30 Questions from chapter five, the red physics book pg 97 Chapter 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

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B. Free Fall 1. 1. Free fall a) a) (one-dimensional) b) b) motion of any object under the influence of gravity only c) c) no air resistance or friction effects of any kind a) a) We are not going to do calculations involving air resistance d) d) If you jump off a chair, you are in free fall.

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2. 2. Galileo discovered (minus air resistance) freely falling objects had the same acceleration. 3. 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. 1. Paper and baseball demo 2. 2. After Galileo Isacc Newton proved Galileos theory 4. 4. Conclusion: magnitude of acceleration is denoted by the symbol: g = 9.81 m/s 2

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4. 4. Review one dimension motion a) a) Orange sheet review b) b) For free fall use the same formulas as before c) c) Now acceleration is g (9.80 m/s 2 ) 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

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Time to play Pascal lab with free fall

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Free Fall problems Chap. 5 questions Pg 106 31-33 Pg 113 66-70, 73 and 74

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formulas v = gt v = gt v = instantaneous speed v = instantaneous speed g = acceleration ( 9.8 m/s 2 ) force of gravity g = acceleration ( 9.8 m/s 2 ) force of gravity t = time t = time Sometimes v=at (a is same as g) Sometimes v=at (a is same as g)

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formulas d = ½ gt 2 d = ½ gt 2 d = distance object falls on the y axis d = distance object falls on the y axis g = acceleration ( 9.8 m/s 2 ) force of gravity g = acceleration ( 9.8 m/s 2 ) force of gravity t 2 = time squared t 2 = time squared ½ (.5) x gt 2 ½ (.5) x gt 2

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problem What would be the velocity of a falling rock starting from rest, 4s, 8s and 15s? What would be the velocity of a falling rock starting from rest, 4s, 8s and 15s? v = (10 m/s 2 ) (0s) = 0m/s v = (10 m/s 2 ) (0s) = 0m/s V = (10 m/s 2 )(4s) = 40m/s V = (10 m/s 2 )(4s) = 40m/s 80m/s and 150m/s 80m/s and 150m/s Position and time Position and time

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problems Find the speed required to throw a ball straight up and have it return 6s later. Neglect air resistance. Find the speed required to throw a ball straight up and have it return 6s later. Neglect air resistance. Hint: v up = v down (3s + 3s) = 6s Hint: v up = v down (3s + 3s) = 6s What is the velocity? What is the velocity? Now solve for distance….. Now solve for distance….. d = ½ gt 2 d = ½ gt 2 Why ½? Why ½? 3 seconds up and 3s seconds down 3 seconds up and 3s seconds down

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Table pg 17 and 20 TimeSpeed/velocitydistance 0s0ms0m 1s10m/s5m 2s20m/s20m 3s30m/s45m 4s40m/s80m 5s50m/s125m tgt ½ gt 2

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Time to play!!! Free fall lab Free fall lab

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