Chapter 11 Motion 2014 -...
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8/26/2014 1 Chapter 11 Motion Section 1 Objectives: Use a frame of reference to describe motion Differentiate between Speed and Velocity Calculate the speed of an object Use graphs to describe speed
Transcript of Chapter 11 Motion 2014 -...
8/26/2014
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Chapter 11 Motion
Section 1
� Objectives:
�Use a frame of reference to describe
motion
�Differentiate between Speed and
Velocity
�Calculate the speed of an object
�Use graphs to describe speed
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Observing Motion
� Motion- an object’s change in
position relative to a reference point.
� Observe objects in relation to other
objects that stay in place.
� Meter – international unit for measuring distance.
= 50 m1 mm
Frame of Reference
� Frame of reference- a system for specifying the precise location of objects in space and time.
� Object that you assume is fixed in place
� Normally you think of walls or signs as not moving, or as being stationary objects
� When you do this you use the walls or signs as a frame of reference?
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Reference Frame� The perception of motion depends on the observer’s
frame of reference
� Objects is in motion when object changes position with respect to a frame of reference.
� Describe the motion observed by one of the boys in the drawing, how does the motion appear to be different to the other boy?
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� Imagine you are the
girl observing the bus,
describe the motion of
each object that you
can see
Frame of Reference
�What do you use as your
frame of reference most
of the time?
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Displacement� Displacement- the change in position of an
object.
� Always includes direction
� Shorter than distance traveled
• In the diagram:
– yellow line =
distance
– black arrow =
displacement
Measuring Motion: Speed
�How do you describe motion taking place?
�To describe motion you discuss speed
�Speed is the distance an object travels per unit of time
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Calculating Speed
� To calculate its speed you divide the distance it travels
by the time it travels
� Speed (S) = distance traveled (d) / the amount of time
it took (t).
S = d/tUnits for speed� Depends, but will always be a distance unit / a time unit
� Ex. Cars: mi./h
� Jets: km/h
� Snails: cm/s
� Falling objects: m/s
SI= m/s
Calculating speed
� If I travel 100 kilometer in one
hour then I have a speed of…
�100 km/h
� If I travel 1 meter in 1 second
then I have a speed of….
�1 m/s
S = d/t
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Calculating Speed
� Speed = Distance Time
� If a runner travels 100 m in 10 seconds what was his average speed?
� Probably not constant
� Can solve for the other pieces too
� Distance = speed x time
� Time = DistanceSpeed
d
V tCover the one you’re looking for
Question
� I travelled 25 km in 10 minutes. How many meters have
I travelled?
� A) 25000 m
� B) .0112 m
� C) .025 m
� D) 2.5 m
25 km * 1000m/km = 25000 m
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Practice� 1. A car race is 500 km long. It takes the winner 2.5
hours to complete it. How fast was he going?
� 2. It is 320 km to Las Vegas. If you average 80 km/hr,
how long will it take you to get there?
� 3. You are going on a trip. You average 80 km/hr for 6
hours. How far did you go?
V=200 km/hourV= 500km
2.5hours
t= 320km
80 km/hrt= 4 hours
d= (80km/hr) x 6 hrs d= 480 km
Constant speed
� A moving object that doesn’t change it’s speed travels at constant speed
� Constant speed means equal distances are covered in an equal amount of time
� Suppose you and a friend want to run around a track at constant speed for half an hour
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Average speed
�Speed is usually NOT CONSTANT
�Ex. Cars stop and go regularly
�Runners go slower uphill than downhill
�Average speed = total distance traveled
total time it took
Calculating Average Speed
� To calculate average speed figure out total distance traveled and divide by total time it took.
� Problem:
• It took me 1 hour to go 40 km on the highway. Then it took me 2 more hours to go 20 km using the streets.
� Total Distance:
� 40 km + 20 km = 60 km
� Total Time:
� 1 h + 2 h = 3 hr
� Ave. Speed:
� total d/total t = 60 km/3 h = 20 km/h
timeTotal
DistTotalSpeedAve
_
._
_. =
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Question� I ran 1000 m in 3 minutes. Then ran another 1000 m
uphill in 7 minutes. What is my average speed?
� A) 100 m/min
� B) 2000 m/min
� C) 10 m/min
� D) 200 m/min
� E) 20 m/min
Total Dist. = 1000 m + 1000 m = 2000 m
Total Time = 3 min + 7 min = 10 min
Ave speed = total dist/total time =
2000m/10 min = 200 m/min = D
Velocity
� An objects speed doesn’t indicate all
there is to know about its motion
� Velocity – the SPEED and DIRECTION of an
object.
� Example:
� An airplane moving North at 500 mph
� A missile moving towards you at 200 m/s
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Measuring Motion: Velocity
� People often use the word speed when they mean velocity
� Speed tells how fast an object moves
� Velocity tells both speed and direction
� Object always travels in some direction
� Velocity is a more precise term for describing motion
� Example: Meteorologists use wind velocity measurements to help predict weather
Velocity
� Is both speed and direction.
� 40 km/hr = speed
� 40 km/hr west = velocity
� Can change velocity two ways
�Change speed
�Change directions
Young male cheetah covered
100 meters east in 7.19 seconds
in a timed run. What is his
velocity?
13.9 m/s east
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� How does this graph display speed?
Graphing Speed:
Distance vs. Time Graphs
Phoenix
Denver
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Graphing Speed:
Distance vs. Time Graphs
Speed = Slope = Rise/
Rise
Graphing Speed:
Distance vs. Time Graphs
Rise=?
3 h
600 km
Speed = Slope = Rise/
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Graphing Speed:
Distance vs. Time Graphs
Rise=?
3 minutes
600 m
Speed = Slope = Rise/
Rise/
Different Slopes
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6 7
Dis
tan
ce
(k
m)
Time (hr)
Run = 1 hr
Run = 1 hr
Run = 1 hr
Rise = 0 km
Rise = 2 km
Rise = 1 km
Slope = Rise/Run= 1 km/1 hr
= 1 km/hr
Slope = Rise/Run= 0 km/1 hr
= 0 km/hr
Slope = Rise/Run= 2 km/1 hr
= 2 km/hr
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Question
� Below is a distance vs. time graph of my
position during a race. What was my
AVERAGE speed for the entire race?
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6
Time (hr)
Dis
tance (km
)Average Speed = Total distance/Total time = 12 km/6 hr
= 2 km/hr
Run = 6 hr
Rise = 12 km
�Why are these graphs different?
�How was the motion different?
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Question
�What does the slope of a
distance vs. time graph
show you about the motion
of an object?
�It tells you the SPEED
Question
� Below is a distance vs. time graph for 3
runners. Who is the fastest?
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 35
Dis
tan
ce (
mi.)
Time (h)
Bob
Jane
Leroy
Leroy is the fastest. He completed the race in 3 hours
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Section 2 Acceleration
�Explain changes that occur
when objects accelerate
�Graph acceleration
Acceleration
� Any change in velocity is
acceleration, even if the speed of
the object remains the same.
� When ever an object changes how it
moves, the velocity changes.
� A change in direction is a change in
velocity, and acceleration.
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Acceleration
�Acceleration – the rate at which velocity changes
�Can be an:
�Increase in speed
�Decrease in speed
�Change in direction
Types of acceleration
� Increasing speed
�Example: Car speeds up at green light
� Decreasing speed
�Example: Car slows down at stop light
� Changing Direction
�Example: Car takes turn (can be at constant speed)
screeeeech
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Question
�How can a car be accelerating
if its speed is a constant 65
km/h?
� If it is changing directions it is
accelerating
Calculating Acceleration
� If an object is moving in a straight line
Time
SpeedInitialspeedFinalonAccelerati
__ −
=
� Units of acceleration:
� m/s2
a= ∆v
t
∆V
a t
a = (Vf)-(Vi)
Time
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Calculating Acceleration
0 s 1 s 2 s 3 s 4 s
0 m/s 4 m/s 8 m/s 12 m/s 16 m/s
Initial Speed Final Speed
a= ∆v
t
Acceleration= Final Speed(Vf)– Initial Speed (Vi)
Time
a= 16 m/s – 0 m/s
4s
a= 4 m/s2
• To calculate acceleration, substrate the difference between
final speed and initial speed. Then divide by time
a= 16 m/s
4s
Question
� A skydiver accelerates from 20 m/s to 40 m/s
in 2 seconds. What is the skydiver’s average
acceleration?
Accel= Final Speed – Initial Speed
Time
= 40m/s – 20 m/s
2s
=20 m/s
2s
= 10m/s2
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Acceleration Practice Problems1. Natalie accelerates her skateboard along a straight path from o m/s to 4.0 m/s
in 2.5 s. Find her average acceleration.
2. A turtle swimming in a straight line toward shore has a speed of 0.50 m/s.
After 4.0s, its speed is 0.80 m/s. What is the turtle’s average acceleration?
3. Mai’s car accelerates at an average rate of 2.6 m/s2. How long will it take her
car to speed up from 24.6 m/s to 26.8 m/s?
Final speed (Vf)= 4.0 m/s
Initial speed (Vi) = 0 m/s
Time=2.5s
a = ?
a= 4.0 m/s – 0 m/s
2.5 s a= 1.6 m/s2
Vf = 0.80 m/s
Vi = 0.50 m/s
Time= 4.0 s
a = ?
a= 0.80 m/s – 0.50 m/s
4.0 s a= 0.075 m/s2
Vf = 26.8 m/sVi = 24.6 m/sTime= ?a= 2.6 m/s2
t= 26.8 m/s – 24.6 m/s
2.6 m/s2t= ∆V
a
t= 0.85 s
Acceleration Practice Problems
4. Tom is driving down I-75. He notices a police officer and slows down from 81
m/s to 62 m/s in 5.0 s. Calculate his acceleration.
5. A cyclist travels at a constant velocity of 4.5 m/s westward and then speeds
up with a steady acceleration of 2.3 m/s2. Calculate the cyclist’s speed after
accelerating for 5.0s.
Vf = Vi + at Vf = 4.5 m/s + (2.3 m/s2 x 5.0 s) Vf = 16 m/s
Vf = 62 m/sVi = 81 m/sTime= 5.0 sa= ?
a= 62 m/s – 81 m/s
5.0 s
a= -19 m/s
5.0 s a= -3.8 m/s2
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Graphing Acceleration
�Can use 2 kinds of graphs
�Speed vs. time
�Distance vs. time
Graphing Acceleration:
Speed vs. Time Graphs
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2
4
6
8
10
12
14
0 1 2 3 4 5 6
Sp
eed
(m
/s)
Time (s)
1) Speed is increasing with time = accelerating
2) Line is straight = acceleration is constant
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Graphing Acceleration:
Speed vs. Time Graphs
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6
Sp
eed
(m
/s)
Time (s)
1) In Speed vs. Time graphs:
Acceleration = Rise/Run
Find the acceleration
= 4 m/s ÷ 2 s = 2 m/s2
Run = 2 s
Rise = 4 m/s
Graphing Acceleration:
Distance vs. Time Graphs
0
5
10
15
20
25
30
35
0 1 2 3 4 5
Dis
tan
ce (
m)
Time (s)
1) On Distance vs. Time graphs a curved line means the object
is accelerating.
2) Curved line also means your speed is increasing. Remember
slope = speed.
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Question
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6
Sp
eed
(m
/s)
Time (s)
Above is a graph showing the speed of a car over time.
1) How is the speed of the car changing (speeding up,
Slowing down, or staying the same)?
2) What is this car’s acceleration?
1) The car is slowing down
2) Acceleration = rise/run = -6m/s ÷3s = -2 m/s2
Run = 3 s
Rise = -6 m/s
Question:
0
5
10
15
20
25
30
35
0 1 2 3 4 5
Time (s)
Dis
tan
ce
(m
)
1)Which line represents an object that is accelerating?
The black and red lines represent a objects that are accelerating. Black is going a greater distance each second, so it must be speeding
up. Red is going less each second, so must be slowing down
Remember: in distance vs. time graphs:
curved line = accelerating, flat line = constant speed
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Question: Hard one
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2
4
6
8
10
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14
0 1 2 3 4 5 6
Time (s)
Sp
ee
d (
m/s
)
Above is a graph showing the speed of a car over time.
1)What would a distance vs. time graph for this
look like?
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6
Dis
tan
ce
(m
)
Time (s)
Understanding the formula
o Acceleration= final velocity- starting velocity
time
o Change in velocity = final – starting
velocity velocity
o Acceleration= change in velocity
time
a= ∆v
t
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Positiveacceleration
Negative
acceleration
Motion in a circle� An object moving in a circle or a curve is constantly
changing direction.
� Centripetal = acceleration towards the center of the
circle.
