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Unit 2 Linear Motion

Unit 2 Linear Motion. I. Outline. Motion defined Position vs. Time Linear Motion Graphing Linear Motion Speed Distance Displacement Velocity Acceleration. A. What is Relative Motion?. A. Motion Defined. Does everything move? How would explain a car moving?

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Unit 2 Linear Motion

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  1. Unit 2 Linear Motion

  2. I. Outline Motion defined Position vs. Time Linear Motion Graphing Linear Motion Speed Distance Displacement Velocity Acceleration

  3. A. What is Relative Motion?

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

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

  6. 1. Position vs. Time • Position location relative to afixed referencepoint • Why a fixed reference point? • 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

  7. B. What is Linear Motion? • Motion means the rate at which something happens. E.g. How fast your car travels down the freeway…or this bird! • Three components of rate: • Speed • Velocity • Acceleration 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?

  8. Simplest form of motion-moving along a straight line or path. • Horizontal or vertical but always a straight path • Position relativeto what? • Movement relative to a motionless point • Earth….. • Sun…… • 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!

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

  10. D. Speed • Speed • Is the measure of how fast (the rate) something is moving • Distance/timee.g. kilometer per hour or (km/h) covered • 50 mph or 30 km/h • Distance = miles • Time hour

  11. Instantaneous Speed: • The speed at any given instant • 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 • Average Speed: ( must be betweenlargest & smallest numbers) • How fast a car will travel over entire distance E.g. trip • Average speed = total distance/ total time interval • Ave. sp. 60 km/h if you traveled 240 km/4 h • What is the speedometer on your car registering? • What is the tachometer on your car registering?

  12. How would you calculate average speed???

  13. Practice Questions • 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? • Would it be possible to attain this average speed and never exceed a reading of 70km/h on the speedometer? d s t

  14. Answers • 35 km/0.5 h = 70 km/h • Average speed=total distance/time interval (or m/s) • 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

  15. E. How would you find distance??? • Distance = average speed X time • 70 km = 35 km/h x 2 hr (km/h x 2hr/1 hours cancel out) 35 kmx2h • h 1 Dist (m) S = d t Time (s) Speed (m/s)

  16. Practice questions • 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

  17. Answer=Distance = average speed x the time interval • 25 m/s X 10 s = • 250m • 25 m/s X 60 s = • 1500m

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

  19. F. One more thing…Displacement • Displacement vs. distance • Displacementis • shortest distance traveled between all the points • “as the crow flies” • Distance is total distance traveled • Driving distance

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

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

  22. Time to Play! Displacement Lab • 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? • Demo with motion sensor, track, and car

  23. G. Velocity • Speed in given direction e.g. 50 mp/h horizontal or vertical. • Velocity is how fastandwhat direction “it” is moving e.g. car, boat, plane etc.

  24. Constant vs. changing velocity • Constant=speed and direction are the same • It isimpossible to detect motion at constant speed. • In a car you detect acceleration and negative acceleration (deceleration) • Changing=one or both are changing e.g. accelerating

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

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

  27. e. Velocity Equation • Average velocity= change in distance/change in time, it is a ratio! • Velocity means m/s • v = ∆d / ∆t • ∆d = d1 or f – d0 • ∆t = t1 or f – t0 • To give us meters per second

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

  29. Displacement Average Velocity • The average velocity equation rearranged • v = ∆d / ∆t • Times each side by ∆t • v ∆t = ∆d • v ∆t = d1 – d0 • Add +d0 to each side to cancel out the minus • d0 + v ∆t = d1

  30. Velocity Questions • A bike travels at a constant speed of 4.0 m/s for 5 s. How far does it go? • Intuitively we know it is 4.0 m/s x 5 s = 20m • Using our equation • v = ∆d / ∆t • Times each side by ∆t • v∆t = ∆d • v∆t = d1 – d0 • Add +d0 to each side to cancel out the minus • d0 + v∆t = d1

  31. V = 4.0 m/s and is constant so no change • ∆t = t1 – t0, which is 5.0 s – 0 s =5 s • d0 = 0 • Therefore: d0 + v∆t = d1 • 0 = (4.0 m/s) (5.0 s) = 20 meters

  32. A bike accelerates from 0.0 m/s to 4.0 m/s in 4.0 s. What distance does it travel? • d0 + v∆t = d1 • 0 + (4.0 m/s) (4 s) = 16 m

  33. H. Acceleration • Acceleration is the rate at which the velocity is changing… • Formula = acceleration =change of speed/time interval • Speed and velocity are measured in units of distance per time d/t (distance and time) • Acceleration equation: • a= ∆v/∆t = v1- v0/t1- t0

  34. Acceleration…Question (concept) • 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?

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

  36. 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! • Acceleration = change of velocity / time interval • ISnegative acceleration real? • YES!

  37. Acceleration Question • 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. • Which undergoes greater acceleration? • What is the acceleration of each vehicle?

  38. Answer • Acceleration = change in speed/time interval • 15 km/h/5s = 3km/h/s • Both are equal acceleration, • rates of change the same • Even thought speeds involved are quite different • V1 – v0/ 5s (time between 2 points)

  39. Time to play…graph matching

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

  41. 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

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

  43. Galileo discovered (minus air resistance) freely falling objects had the same acceleration. • 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 • Paper and baseball demo • After Galileo Isacc Newton proved Galileo’s theory • Conclusion: magnitude of acceleration is denoted by the symbol: • g = 9.81 m/s2

  44. Review one dimension motion • Orange sheet review • For free fall use the same formulas as before • 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

  45. Time to play • Pascal lab with free fall

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

  47. formulas • v = gt • v = instantaneous speed • g = acceleration ( 9.8 m/s2 ) force of gravity • t = time • Sometimes v=at (a is same as g)

  48. formulas • d = ½ gt2 • d = distance object falls on the y axis • g = acceleration ( 9.8 m/s2 ) force of gravity • t2 = time squared • ½ (.5) x gt2

  49. problem • What would be the velocity of a falling rock starting from rest, 4s, 8s and 15s? • v = (10 m/s2 ) (0s) = 0m/s • V = (10 m/s2 )(4s) = 40m/s • 80m/s and 150m/s • Position and time

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