UNIT 2 A LINEAR MOTION Unit 2 A

UNIT 2 A LINEAR MOTION

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

2. 1 Motion 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 position relative to a fixed point is changing.

2. 1 Motion 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 speeds of things on Earth are usually measured relative to the Earth’s surface.

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. Reference point Motion

2. 2 Speed 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. distance speed = time 5 mi avg. speed = 0. 20 h avg. speed = 25 mi/h

2. 2 Speed

2. 2 Speed Instantaneous Speed 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 average speed: total distance time

2. 2 Speed If we know average speed and travel time, the distance traveled is easy to find. distance speed = time distance = speed x time 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 320 km

2. 2 Speed 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 250 m distance = speed x time In 1 minute? distance = (25 m) x (x m) (1 s) (60 s) = 1500 m

2. 2 Speed 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 speed = = time 35 km 0. 5 h = 70 km/h

Quick Quiz! 1. 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 ___. A. 2 m/s B. 5 m/s C. 8 m/s D. 12 m/s 2. 1

Quick Quiz. 2. A gazelle travels 2 km in a half hour. The gazelle’s average speed is ___. A. 1/2 km/h B. 1 km/h C. 2 km/h D. 4 km/h 2. 2

2. 3 Velocity 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) m ∆d (m/s) v= t t s

2. 3 Velocity If either the speed or the direction (or both) changes, then the velocity changes. • constant speed and constant velocity are NOT the same. The car speedometer always reads 30 km/h. Is speed constant? Y Is velocity constant? N

2. 4 Acceleration We can change an object’s motion by changing its speed, its direction, or both. Acceleration is the rate at which velocity changes. ∆v (v – v ) a= t f t i acceleration can increase or decrease speed,

2. 4 Acceleration We can change an object’s motion by changing its speed, its direction, or both. Acceleration: is the rate at which velocity changes. ∆v (v – v ) a= t f t i acceleration can increase or decrease speed, deceleration is really negative acceleration (–a)

2. 4 Acceleration concerns change in velocity so any a change in direction is acceleration. The car speedometer always reads 30 km/h. Is velocity constant? N Is there an acceleration? Y

2. 4 Acceleration a in the same direction as v : speed up

2. 4 Acceleration a in the same direction as v : speed up a in the opp. direction as v : slow down

2. 4 Acceleration 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

2. 4 Acceleration v units are in distance per time: (m/s) • a is the change in v per change in time. ∆v a= t m/s or m s s 2 • a units are v per time: (m/s per s) or (m/s 2) • changing v from 0 m/s to 10 m/s in 1 s, a is… 10 m/s – 0 m/s 10 m/s a= = = 10 m/s 2 1 s 1 s

2. 4 Acceleration 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 10 m/s acar = = = 2 m/s 2 5 s 5 s 10 m/s – 0 m/s 10 m/s atruck = = = 2 m/s 2 5 s 5 s

Quick Quiz! 1. Constant speed in a constant direction is… A. constant velocity. B. constant acceleration. C. instantaneous speed. D. average velocity. 2. 3

Quick Quiz. 2. A vehicle undergoes acceleration when it __. A. gains speed. B. decreases speed. C. changes direction. D. ALL of the above 2. 4

2. 5 Free 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/s 2.

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

2. 5 Free 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 to 0 m/s. v = 0 m/s at hmax • a = ? a = – 10 m/s 2 = g • It then falls downward as if it had been dropped from rest, going from 0 m/s back to vi (but downward) • a = ? a = – 10 m/s 2 = g vo

2. 5 Free 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/s 2)(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/s 2)(8 s) v = – 100 m/s

2. 8 Air Resistance and Falling Objects Drop a feather and a coin and the coin reaches the floor far ahead of the feather. Why? Air resistance is responsible for these different accelerations. (not just g) In a vacuum, the feather and coin fall with exactly the same acceleration, g. With what objects might air resistance be small enough to be ignored?

2. 6 Free 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/s 2 v = vi + at (a is g) t = 3 s, v = 30 m/s, d = 45 m vavg = (30 + 40) 2 d = 35 m 1 s vavg = 35 m/s t = 4 s, v = 40 m/s, d = 80 m d = vit + ½at 2 1 s vavg = (40 + 50) 2 d = 45 m vavg = 45 m/s t = 5 s, v = 50 m/s, d = 125 m

2. 6 Free 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/s 2)(3 s) v = 30 m/s What is its vavg during the 3 s? vavg = (vf + vi) vavg = 15 m/s 2 vavg = (0 m/s + 30 m/s) 2 1 s 2 s 3 s

2. 6 Free 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 + ½at 2 (a is g) 1 s d = (0 m/s)(3 s) + ½(10 m/s 2)(3 s)2 d = 45 m 2 s 3 s

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 at 2

Linear Motion - Practice Problems 2) Find the uniform acceleration that causes a car’s velocity to change from 32 m/s to 96 m/s in an 8. 0 s period. vf = vi + at 3) A car with a velocity of 22 m/s is accelerated uniformly at a rate of 1. 6 m/s for 6. 8 s. What is the final velocity? vf = vi + at

Linear Motion - Practice Problems 4) An airplane starts from rest and accelerates at a constant 3. 0 m/s 2 for 30 s before leaving the ground. a) How far did it move? b) How fast was it going at liftoff? d = vi t + ½ at 2 vf = vi + at

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 + 1/2 at

Quick Quiz! 1. In a vacuum tube, a feather is seen to fall as fast as a coin. This is because … A. gravity doesn’t act in a vacuum. B. air resistance doesn’t act in a vacuum. C. greater air resistance acts on the coin. D. gravity is greater in a vacuum. 2. 8

Quick Quiz. 2. If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as _____. A. 10 m/s/s B. 10 m/s 2 C. v = gt D. both A and B 2. 5

Quick Quiz. d = vit + ½at 2 3. A rock falls 180 m from a cliff into the ocean. How long is it in free fall? A. 6 s 180 = (0)t + ½(10)t 2 B. 10 s 180 = ½(10)t 2 C. 18 s 180 = 5 t 2 180 = t 2 D. 180 s 5 36 = t 2 √ 36 = t t=6 s 2. 6

2. 7 Graphs of Motion Equations, tables, and pictures are not the only way to describe relationships between distance, velocity, and acceleration. Graphs can visually describe relationships.

2. 7 Graphs of Motion distance (m) distance vs. time: constant velocity (a = 0) slope = distance = v time (s)

2. 7 Graphs of Motion distance (m) distance vs. time: constant acceleration (+a) slope = distance = v time (s) parabolic curve b/c time is squared (quadratic) d = ½at 2

2. 7 Graphs of Motion distance vs. time d v: + 2 d 1 dir: → fast dir: → v: + slow a: 0 t dir: ← v: – 4 dir: ← v: – d d 3 fast slow t a: 0

distance (m) 2. 7 Graphs of Motion Describe the motion. v: 0 a: 0 v: + a: 0 time (s) • moves forward at v = 5 m/s for 5 s. • stops at 25 m (v = 0 m/s) for 5 s.

2. 7 Graphs of Motion velocity (m/s) velocity vs. time: constant velocity (a = 0) slope = velocity = a time (s)

2. 7 Graphs of Motion velocity (m/s) velocity vs. time: constant acceleration (+a) slope = velocity = a time (s)

2. 7 Graphs of Motion dir: right v : + (constant) a : 0 dir: right v : + (faster) a: + dir: left v : – (slower) a : + dir: left v : – (constant) a : 0 dir: right v : + (slower) a : – dir: left v : – (faster) a : –

2. 7 Graphs of Motion Consider the graph below. Describe the motion. (include all that are true): A. B. C. D. E. F. G. H. I. J. moving forward constant velocity positive velocity negative velocity slowing down changing directions speeding up positive acceleration constant acceleration negative acceleration + v 0 – t

Quick Quiz! The slope of a velocity-versus-time graph represents ____. A. distance B. velocity C. acceleration D. time

WARM UP Consider the graph below. Describe the motion from. . . A. t = 0 -1 s B. t = 1 -4 s C. t = 4 -9 s D. t = 9 -12 s v=– v=+ v=+ a=– a=+ a=– ←, faster →, slower At what time is v = 0 m/s at 9 s

Equations Summary N NOT given on test distance speed = time N ∆d v= t v = vi + at vavg = (vf + vi) 2 ∆v a= t d = vit + ½at 2 given on test g = – 10 m/s 2

WS Motion Graphs Begin your worksheet now. We will take all of class tomorrow to finish it.

2. 7 Graphs of Motion distance vs. time v : __ d 1 dir: __ d _____ a : __ t 2 dir: __ v : __ ____ a : __ t 3 dir: __ v : __ _____ a : __ d d t t 4 dir: __ v : __ _____ a : __

2. 7 Graphs of Motion dir: _____ v : __ (______) a : __ velocity vs. time dir: _____ v : __ (______) a : __ dir: _____ v : __ (______) a : __

https: //www. youtube. com/watch? v=r. D 0 tmg. Mdb. Qg VIDEO – Part 1 (7: 19) Acceleration & Velocity Graphs

https: //www. youtube. com/watch? v=JFZ 2 W 5 Pwlr. Y VIDEO – Part 2 (9: 53) Acceleration & Velocity Graphs

https: //www. youtube. com/watch? v=n. Ph. Rrhb 99 r. Y VIDEO – Part 3 (7: 45) Acceleration & Velocity Graphs