l inear m otion unit 2a. distance | speed | direction acceleration unit 2a: linear motion (chap 2)...
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LINEAR MOTIONLINEAR MOTION
UNIT 2AUNIT 2A
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distance | speed | direction acceleration
Unit 2AUnit 2A: : Linear MotionLinear Motion (Chap 2)
You can describe the motion of an object by its:
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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 about30 km/s relative to the sun.
2.1 Motion Is Relative
An object is moving if its position relative to a fixed point is changing.
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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.
2.1 Motion Is Relative
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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.
You have set yourself as the reference point as the car rolls slightly backward.
WHAT??
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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.
2.2 Speed
speed =
distance
time
avg. speed =
5 mi
0.20 h
avg. speed = 25 mi/h
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2.2 Speed
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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
2.2 Speed
average speed: total distance time
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If we know average speed and travel time, the distance traveled is easy to find.
ExampleExample: If your average speed is 80 km/h on : If your average speed is 80 km/h on a 4-hour trip, then how far did you travel?a 4-hour trip, then how far did you travel?
distance = distance = 80 km80 km = x km = x km 1 h1 h 4 hr 4 hr
2.2 Speed
speed =
distance
time
distance = speed x time
320 km320 km
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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)
2.2 Speed
250 m
1500 m
distance = speed x time
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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?
2.2 Speed
speed =
distance
time=
35 km
0.5 h=
70 km/h
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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
Quick Quiz!
2.1
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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
Quick Quiz.
2.2
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In physics,
Velocity: is speed in a direction.direction.
• speed: 60 km/h
• velocity: 60 km/h north, or right, or down…
2.3 Velocity
v =
∆dt
∆: change in… (final – initial)
(df – di) t
ms
(m/s)
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If either the speed or the direction (or both)changes, then the velocity changes.
• constant speed and constant velocity are NOT the same.
2.3 Velocity
The car speedometer always reads 30 km/h.
Is speed constant?
Is velocity constant?
Y
N
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We can change an object’s motion by changingits speed, its direction, or both.
Acceleration is the rate at which velocity changes.
2.4 Acceleration
a =
∆vt
(vf – vi) t
acceleration can increase or decrease speed,
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We can change an object’s motion by changing its speed, its direction, or both.
Acceleration: is the rate at which velocity changes.
2.4 Acceleration
a =
∆vt
(vf – vi) t
acceleration can increase or decrease speed,deceleration is really negative acceleration (–a)
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Acceleration concerns change in velocity so any a change in direction is acceleration.
2.4 Acceleration
The car speedometer always reads 30 km/h.
Is velocity constant?
Is there an acceleration?
N
Y
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2.4 Acceleration
a in the same direction as v : speed up
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2.4 Acceleration
a in the same direction as v : speed upa in the opp. direction as v : slow down
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a in the same direction as v : speed up
2.4 Acceleration
a in the opp. direction as v : slow downa at an angle to v : change direction
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v units are in distance per time: (m/s)
• a is the change in v per change in time.
• a units 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…
2.4 Acceleration
a =
∆vt
m/ss
m s2
or
a =
10 m/s – 0 m/s 1 s
=
10 m/s1 s
10 m/s2=
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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?
2.4 Acceleration
acar = 18 m/s – 8 m/s
5 s=
10 m/s5 s
2 m/s2=
atruck = 10 m/s – 0 m/s
5 s=
10 m/s5 s
2 m/s2=
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1. Constant speed in a constant direction is…
A. constant velocity.
B. constant acceleration.
C. instantaneous speed.
D.average velocity.
Quick Quiz!
2.3
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2. A vehicle undergoes acceleration when it __.
A. gains speed.
B. decreases speed.
C. changes direction.
D. ALL of the above
Quick Quiz.
2.4
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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.
2.5 Free Fall: How Fast
During each 1 s of fall, v increases by 10 m/s.
This gain in v in m/sis a in m/s2.
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2.5 Free Fall: How Fastt = 0 s, v = 0 m/st = 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
t = 5 s, v = 50 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
g = –10 m/s2
v = vi + at (a is g)
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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.
• a = ?
• It then falls downward as if it had been dropped from rest,going from 0 m/s back to vi (but downward)
• a = ?
2.5 Free Fall: How Fast
v = 0 m/s at hmax vo a = –10 m/s2 = g
a = –10 m/s2 = g
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What would the speedometer reading on the falling rock be 4.5 seconds after it drops from rest? (v = ?)
2.5 Free Fall: How Fast
How about 8 seconds after it is thrown with an initial velocity of 20 m/s downward?
v = vi + atv = 0 m/s + (–10 m/s2)(4.5 s)
v = –45.0 m/s
v = –20 m/s + (–10 m/s2)(8 s)
v = –100 m/s
(a is g)
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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.
2.8 Air Resistance and Falling Objects
With what objects might air resistance be small enough to be ignored?
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2.6 Free Fall: How Fart = 0 s, v = 0 m/s, d = 0 m
g = –10 m/s2
v = vi + at
t = 1 s, v = 10 m/s, d = 5 m
t = 2 s, v = 20 m/s, d = 20 m
t = 3 s, v = 30 m/s, d = 45 m
t = 4 s, v = 40 m/s, d = 80 m
t = 5 s, v = 50 m/s, d = 125 m
d = vit + ½at2
d = 35 m
vavg = (30 + 40) 2vavg = 35 m/s
1 s
d = 45 m
vavg = (40 + 50) 2vavg = 45 m/s1 s
(a is g)
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An apple falls to the ground in 3 s.
What is its speed upon striking the ground?
2.6 Free Fall: How Far
vf = vi + atv = 0 m/s + (10 m/s2)(3 s)
v = 30 m/s
vavg = (0 m/s + 30 m/s) 2
vavg = 15 m/svavg = (vf + vi) 2
1 s
2 s
3 s
What is its vavg during the 3 s?
(a is g)
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An apple falls to the ground in 3 s.
How high above ground was the apple when it first dropped?
2.6 Free Fall: How Far
d = vit + ½at2
v = 30 m/s
vavg = 15 m/s
d = (0 m/s)(3 s) + ½(10 m/s2)(3 s)2
d = 45 m
1 s
2 s
3 s
(a is g)
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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
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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
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Linear Motion - Practice Problems
4) An airplane starts from rest and accelerates at a constant 3.0m/s2 for 30s before leaving the ground. a)How far did it move?b)How fast was it going at liftoff?
d = vi t + ½ at2
vf = vi + at
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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
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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.
Quick Quiz!
2.8
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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/s2
C.v = gt
D.both A and B
Quick Quiz.
2.5
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3. A rock falls 180 m from a cliff into the ocean. How long is it in free fall?
A. 6 s
B. 10 s
C.18 s
D.180 s
Quick Quiz.
2.6
d = vit + ½at2
180 = (0)t + ½(10)t2
180 = ½(10)t2
180 = 5t2
180 = t2
5
36 = t2
√36 = t t = 6 s
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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
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distance vs. time:
2.7 Graphs of Motiond
ista
nce
(m
)
time (s)
slope = distance = v time
constant velocity (a = 0)
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distance vs. time:
2.7 Graphs of Motiond
ista
nce
(m
)
time (s)
slope = distance = v time
parabolic curve b/c time is squared(quadratic)
d = ½at2
constant acceleration (+a)
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2.7 Graphs of Motiond
t
d
t
d
t
distance vs. time
dir:v :
a :
1
3
2 →+
fast
0
dir:v :
a :
→+
slow
0
dir:v :
a :
←–
slow
0
dir:v :
a :
←–
fast
0
4d
t
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2.7 Graphs of Motiond
ista
nce
(m
)
time (s)
Describe the motion.
v : +
a : 0
v : 0
a : 0
• moves forward at v = 5 m/s for 5 s.• stops at 25 m (v = 0 m/s) for 5 s.
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velocity vs. time: constant velocity (a = 0)2.7 Graphs of Motion
velo
city
(m
/s)
time (s)
slope = velocity = a time
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velocity vs. time: constant acceleration (+a)2.7 Graphs of Motion
velo
city
(m
/s)
time (s)
slope = velocity = a time
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2.7 Graphs of Motion
dir: v : a :
right+ (constant) 0
dir: v : a :
left– (constant) 0
dir: v : a :
right+ (faster) +
dir: v : a :
left– (slower) +
right+ (slower) –
dir: v : a :
left– (faster) –
dir: v : a :
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2.7 Graphs of Motion
tv
+
–
0
Consider the graph below. Describe the motion.(include all that are true):
A.moving forward
B.constant velocity
C.positive velocity
D.negative velocity
E.slowing down
F.changing directions
G.speeding up
H.positive acceleration
I.constant acceleration
J.negative acceleration
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The slope of a velocity-versus-time graph represents ____.
A. distance
B. velocity
C. acceleration
D. time
Quick Quiz!
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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 =
a =
→, faster
+
+ v =
a =
→, faster
v =
a =
→, slower
+
+
+
– v =
a =
←, faster
–
–
WARM UPWARM UP
At what time
is v = 0 m/sv = 0 m/s at 9 s
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Equations Summary
speed =
distance
time
v =
∆d
t
a =
∆v
t
v = vi + at vavg = (vf + vi)
2
d = vit + ½at2 g = –10 m/s2
NOT
given on test
given on test
NN
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WS Motion Graphs
Begin your worksheet now.
We will take all of class tomorrow to finish it.
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2.7 Graphs of Motiond
t
d
t
d
t
distance vs. time
1
3
2dir:v :
a :
____
_____
__
dir:v :
a :
____
____
__
dir:v :
a :
____
_____
__
d
t
dir:v :
a :
____
_____
__
4
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_______ (______) __
2.7 Graphs of Motion
dir: v : a :
_______ (______) __
dir: v : a :
_______ (______) __
_______ (______)
__
dir: v : a :
dir: v : a :
_______ (______) __
_______ (______)
__
dir: v : a :
dir: v : a :
velocity vs. time
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https://www.youtube.com/watch?v=rD0tmgMdbQg
VIDEO – Part 1(7:19)
Acceleration & Velocity Acceleration & Velocity GraphsGraphs
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https://www.youtube.com/watch?v=JFZ2W5PwlrY
VIDEO – Part 2(9:53)
Acceleration & Velocity Acceleration & Velocity GraphsGraphs
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https://www.youtube.com/watch?v=nPhRrhb99rY
VIDEO – Part 3(7:45)
Acceleration & Velocity Acceleration & Velocity GraphsGraphs