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Linear Motion

UNIT 2A. Linear Motion. Unit 2A : Linear Motion (Chap 2). distance | speed | direction acceleration. You can describe the motion of an object by its:. 2.1 Motion Is Relative. How do you know if an object is moving ? Is your book moving? The book is at rest,

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Linear Motion

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  1. UNIT 2A Linear Motion

  2. Unit 2A: Linear Motion (Chap 2) distance | speed | direction acceleration You can describe the motion of an object by its:

  3. 2.1Motion Is Relative How do you know if an object is moving? • Is your book moving? The book is at rest, relative to the table, BUT It’s moving at about 30 km/s relative to the sun. An object is moving if its positionrelative to a fixedpoint is changing.

  4. 2.1Motion Is Relative An object’s motion must be described relative to something else. • shuttle 8 km/s relative to Earth below • race car 300 km/h relative to the track • The speedsof things on Earth are usuallymeasuredrelativeto the Earth’ssurface.

  5. Reference point Motion Problem: You are a passenger in a car stopped at a stop sign. Out of the corner of your eye, you notice a tree on the side of the road begin to move forward. WHAT?? You have set yourself as the reference point as the car rolls slightly backward.

  6. 2.2Speed 400 yrs ago, people described motion as simply “slow” or “fast.” Galileo was the first to measure speed by the distance covered and the time it takes. 5 mi 0.20 h distance time avg. speed = speed = 25 mi/h avg. speed =

  7. 2.2Speed

  8. 2.2Speed Cars do not always move at a constant speed. You can tell the speed of the car at any instant by looking at the car’s speedometer. instantaneous speed: the speed at any instant Instantaneous Speed average speed: total distance time

  9. 2.2Speed If we know average speed and travel time, the distance traveled is easy to find. Example: If your average speed is 80 km/h on a 4-hour trip, then how far did you travel? distance = 80 km = x km 1 h 4 hr distance time speed = distance = speed x time 320 km

  10. 2.2Speed If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? distance = (25 m) = (x m) = (1 s) 10 s In 1 minute? distance = (25 m) x (x m) = (1 s) (60 s) 250 m distance = speed x time 1500 m

  11. 2.2Speed The speedometer in every car also has an odometer that records the distance traveled. If the odometer reads zero at the beginning of a trip and 35 km a half hour later, what is the average speed? distance time 35 km 0.5 h speed = = = 70 km/h

  12. Quick Quiz! • Jake walks east through a passenger car on a train that moves 10 m/s in the same direction. Jake’s speed relative to the car is 2 m/s. Jake’s speed relative to an observer at rest outside the train is ___. • 2 m/s • 5 m/s • 8 m/s • 12 m/s 2.1

  13. Quick Quiz. • A gazelle travels 2 km in a half hour. The gazelle’s average speed is ___. • 1/2 km/h • 1 km/h • 2 km/h • 4 km/h 2.2

  14. 2.3Velocity In physics, Velocity:is speed in a direction. • speed: 60 km/h • velocity: 60 km/h north, or right, or down… ∆: change in… (final – initial) (df – di) t ∆d t m s (m/s) v =

  15. 2.3Velocity If either the speedorthe direction (or both) changes, then the velocitychanges. • constant speed and constant velocity are NOT the same. The car speedometer always reads 30 km/h. Is speed constant? Is velocity constant? Y N

  16. 2.4Acceleration We can change an object’s motion by changing its speed, its direction, or both. Accelerationis the rate at which velocitychanges. ∆v t (vf – vi) t a = acceleration can increaseordecrease speed,

  17. 2.4Acceleration We can change an object’s motion by changing its speed, its direction, or both. Acceleration:is the rate at which velocitychanges. ∆v t (vf – vi) t a = acceleration can increaseordecrease speed, deceleration is really negativeacceleration (–a)

  18. 2.4Acceleration Acceleration concerns change in velocity so any a change in directionis acceleration. The car speedometer always reads 30 km/h. Is velocity constant? Is there an acceleration? N Y

  19. 2.4Acceleration a in the same direction as v:speed up

  20. 2.4Acceleration a in the same direction as v:speed up a in the opp. direction as v:slow down

  21. 2.4Acceleration a in the same direction as v:speed up a in the opp. direction as v:slow down a at an angle to v:change direction

  22. 2.4Acceleration vunits are in distance per time: (m/s) • a is the change in v per change in time. • aunits are v per time: (m/s per s) or (m/s2) • changing v from 0 m/s to 10 m/s in 1 s, a is… ∆v t m/s s m s2 or a = 10 m/s – 0 m/s 1 s 10 m/s 1 s a = 10 m/s2 = =

  23. 2.4Acceleration In 5 seconds a car increases its speed from 8 m/s to 18 m/s, while a truck goes from rest to 10 m/s in a straight line. Which undergoes greater acceleration? 18 m/s – 8 m/s 5 s 10 m/s 5 s acar = 2 m/s2 = = 10 m/s – 0 m/s 5 s 10 m/s 5 s atruck = 2 m/s2 = =

  24. Quick Quiz! • Constant speed in a constant direction is… • constant velocity. • constant acceleration. • instantaneous speed. • average velocity. 2.3

  25. Quick Quiz. • A vehicle undergoes acceleration when it __. • gains speed. • decreases speed. • changes direction. • ALL of the above 2.4

  26. 2.5Free Fall: How Fast Imagine there is no air resistance and that gravity is the only thing affecting a falling object. • An object moving under influence of the gravitational force only is said to be in free fall. During each 1 s of fall, v increases by 10 m/s. This gain in v in m/s is a in m/s2.

  27. 2.5Free Fall: How Fast t = 0 s, v = 0 m/s g is used for the acceleration due to gravity Although g varies slightly based on altitude, its average value is nearly 10 m/s2 t = 1 s, v = 10 m/s t = 2 s, v = 20 m/s t = 3 s, v = 30 m/s t = 4 s, v = 40 m/s g = –10 m/s2 v = vi + at (a is g) t = 5 s, v = 50 m/s

  28. 2.5Free Fall: How Fast An object is thrown straight up: • It moves upward for a while. • What is v at its highest point? • Going up, vi goes to0 m/s. • a =? • It then falls downward as if it had been dropped from rest, going from 0 m/s back to vi (but downward) • a =? v = 0 m/s at hmax vo a= –10 m/s2 =g a= –10 m/s2 =g

  29. 2.5Free Fall: How Fast What would the speedometer reading on the falling rock be 4.5 seconds after it drops from rest? (v = ?) v = vi + at v = 0 m/s + (–10 m/s2)(4.5 s) (a is g) v = –45.0 m/s How about 8 seconds after it is thrown with an initial velocity of 20 m/s downward? v = –20 m/s + (–10 m/s2)(8 s) v = –100 m/s

  30. 2.8Air Resistance and Falling Objects Drop a feather and a coin and the coin reaches the floor far ahead of the feather. Why? Air resistanceis responsible for these different accelerations. (not just g) In a vacuum, the feather and coin fall with exactly the sameacceleration, g. With what objects might air resistance be small enough to be ignored?

  31. 2.6Free Fall: How Far t = 0 s, v = 0 m/s, d = 0 m t = 1 s, v = 10 m/s, d = 5 m t = 2 s, v = 20 m/s, d = 20 m g = –10 m/s2 t = 3 s, v = 30 m/s, d = 45 m vavg = (30 + 40) 2 vavg = 35 m/s d = 35 m 1 s v = vi + at t = 4 s, v = 40 m/s, d = 80 m (a is g) d = vit + ½at2 vavg = (40 + 50) 2 vavg = 45 m/s d = 45 m 1 s t = 5 s, v = 50 m/s, d = 125 m

  32. 2.6Free Fall: How Far An apple falls to the ground in 3 s. What is its speed upon striking the ground? vf = vi + at (a is g) v = 0 m/s + (10 m/s2)(3 s) v = 30 m/s What is its vavg during the 3 s? 1 s vavg = (vf + vi) 2 vavg = 15 m/s 2 s vavg = (0 m/s + 30 m/s) 2 3 s

  33. 2.6Free Fall: How Far An apple falls to the ground in 3 s. How high above ground was the apple when it first dropped? v = 30 m/s vavg = 15 m/s d = vit + ½at2 (a is g) 1 s d = (0 m/s)(3 s) + ½(10 m/s2)(3 s)2 2 s d = 45 m 3 s

  34. Linear Motion - Practice Problems 1) An angry mob lynches a physics teacher after receiving their grades. They throw the physics teacher off a tall building straight down with a velocity of 20 m/s. The teacher falls for 3.0 seconds landing on a stack cardboard boxes. From what height was he thrown? d = vi t + ½ at2

  35. Linear Motion - Practice Problems 2) Find the uniform acceleration that causes a car’s velocity to change from 32m/s to 96m/s in an 8.0s period. 3) A car with a velocity of 22m/s is accelerated uniformly at a rate of 1.6m/s for 6.8s. What is the final velocity? vf = vi + at vf = vi + at

  36. Linear Motion - Practice Problems 4) An airplane starts from rest and accelerates at a constant 3.0m/s2 for 30s before leaving the ground. • How far did it move? • How fast was it going at liftoff? d = vi t + ½ at2 vf = vi + at

  37. Linear Motion - Practice Problems 5) Your sister drops your house keys down to you from the second floor window. If you catch them 4.3 m from where your sister dropped them, what is the velocity of the keys when you catch them? d = vit + 1/2at

  38. Quick Quiz! • In a vacuum tube, a feather is seen to fall as fast as a coin. This is because … • gravity doesn’t act in a vacuum. • air resistance doesn’t act in a vacuum. • greater air resistance acts on the coin. • gravity is greater in a vacuum. 2.8

  39. Quick Quiz. • If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as _________. • 10 m/s/s • 10 m/s2 • v = gt • both A and B 2.5

  40. d = vit + ½at2 Quick Quiz. • A rock falls 180 m from a cliff into the ocean. How long is it in free fall? • 6 s • 10 s • 18 s • 180 s 180 = (0)t + ½(10)t2 180 = ½(10)t2 180 = 5t2 180 = t2 5 36 = t2 √36 = t t = 6 s 2.6

  41. 2.7Graphs of Motion Equations, tables, and pictures are not the only way to describe relationships between distance, velocity, and acceleration. Graphs can visually describe relationships.

  42. 2.7Graphs of Motion distance vs. time: constant velocity (a= 0) slope = distance = v time distance (m) time (s)

  43. 2.7Graphs of Motion distance vs. time: constant acceleration (+a) parabolic curve b/c time is squared (quadratic) d = ½at2 slope = distance = v time distance (m) time (s)

  44. 2.7Graphs of Motion distance vs. time 1 2 dir:v : a : → + fast 0 dir:v : a : → + slow 0 d d t t 3 4 dir:v : a : ← – fast 0 dir:v : a : ← – slow 0 d d t t

  45. Describe the motion. 2.7Graphs of Motion v : 0 a : 0 v : + a : 0 distance (m) time (s) • moves forward at v = 5 m/s for 5 s. • stops at 25 m (v = 0 m/s) for 5 s.

  46. 2.7Graphs of Motion velocity vs. time: constant velocity(a= 0) slope = velocity = a time velocity (m/s) time (s)

  47. 2.7Graphs of Motion velocity vs. time: constant acceleration (+a) velocity (m/s) slope = velocity = a time time (s)

  48. 2.7Graphs of Motion dir: v : a : dir: v : a : right + (constant) 0 left – (constant) 0 dir: v : a : right + (faster) + dir: v : a : right + (slower) – left – (faster) – dir: v : a : dir: v : a : left – (slower) +

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