• Claim : A statement that responds to the
question asked or the problem posed.
• Evidence: Scientific data used to support the
claim
• Reasoning: Using scientific principles to show
why data count as evidence to support the
claim.
9/9
1. How could you use the labquest photogates
to measure the speed of your finger?
2. How is it possible to be going at 200 mph and
staying still at the same time?
You can describe the motion
of an object by its position,
speed, direction, and
acceleration.
4.1 Motion Is Relative
Even things that appear to be at rest move.
When we describe the motion of one object with respect to
another, we say that the object is moving relative to the
other object.
A book that is at rest, relative to the table it lies on, is
moving at about 30 kilometers per second relative to
the sun.
The book moves even faster relative to the center of our
galaxy.
4.1 Motion Is Relative
The racing cars in the Indy 500 move relative to the track.
4.1 Motion Is Relative
When we discuss the motion of something, we describe its
motion relative to something else.
The space shuttle moves at 8 kilometers per second
relative to Earth below.
A racing car in the Indy 500 reaches a speed of 300
kilometers per hour relative to the track.
Unless stated otherwise, the speeds of things in our
environment are measured relative to the surface of
Earth.
4.2 Speed
We will primarily use the unit meters per second (m/s) for
speed.
If a cheetah covers 50 meters in a time of 2 seconds, its speed
is 25 m/s.
4.1 Motion Is Relative
Although you may be at rest relative to Earth’s surface,
you’re moving about 100,000 km/h relative to the sun.
4.2 Speed
Before the time of Galileo, people described moving things as
simply “slow” or “fast.” Such descriptions were vague.
Galileo is credited as being the first to measure speed by
considering the distance covered and the time it takes.
Speed is how fast an object is moving.
Motion vocab
• Displacement – change in position
• Speed – distance over time
• Velocity – displacement / time
• Or speed plus direction
Acceleration = Change in velocity / time
4.2 Speed
The speedometer gives readings of instantaneous speed in both mi/h and km/h.
4.2 Speed
Average Speed
In a trip by car, the car will certainly not travel at the
same speed all during the trip.
The driver cares about the average speed for the trip as
a whole.
The average speed is the total distance covered divided
by the time.
Steps to problem solving
•
•
•
•
1. What is the problem asking
2. What are your givens
3. Which equation are you going to use?
4. plug in numbers to the equation and solve
9/10
• See displacement velocity and acceleration
google presentation
• Whiteboarding graphs
9/11
• Construct three graphs (position vs time, velocity
vs time, acceleration versus time) of a person
walking down the hall at a constant rate.
• What does the slope of a position time graph tell
you?
• What does the slope of a velocity time graph tell
you?
Agenda
- Turn in speed problems
- Speed lab
9/14
• Marsell the shell went 2 cm in 2 seconds stopped
for another 4 seconds then moved 4 cm in 2
seconds.
• 1. How many total seconds should be in the xaxis?
• 2. Construct a position vs time graph, a velocity
versus time graph.
• What is the instantaneous velocity at 3
seconds?
• . The positions of runner 1 and runner 2 are shown above
at each second.
•
• During what time interval do the runners have the same
average velocity?
• A. Between 0 and 2 seconds
• B. Between 0 and 3 seconds
• C. Between 0 and 4 seconds
x
curve
up
x
t
v
curve
down
x
t
flat line
v
flat
line
x
t
flat line
t
constant above
zero
v
constant
v
0
0
t
t
t
t
constant above
a
zero
a
a
constant
equal to zero
constant below
zero
t
t
a
0
t
t
Speed up
(+) acceleration
Slow Down
(-) acceleration
Constant Speed
(0) acceleration
-moving away (+x)
Not moving
No velocity
No acceleration
• Dependent variable – the thing that
changes as a result
• Independent variable – one thing that
influences another
How to set up your graph!
How to set up your graph!
Y Axis
(This is for your
dependent
variable)
How to set up your graph!
X Axis
(This is for your
independent variable)
Let’s Learn About Graphs.
There are many different types of graphs.
Let’s learn about two kinds.
1. The bar graph
100
90
80
70
60
50
40
30
20
10
0
Math
Reading
10 0
90
80
70
60
2. The line graph
50
40
30
20
10
0
M ath
Reading
S ci
SS
L. A rts
Sci
SS
L. Arts
How to determine scale
Favorite
food
Number of
Teachers
Mexican
22
Spaghetti
15
cheeseburger 11
Sushi
5
Don’t eat
2
• Scale is determined
by your highest &
lowest number.
• In this case your
scale would be from
2 – 22.
How to determine Intervals
Favorite
food
Number of
Teachers
Mexican
22
Spaghetti
15
cheeseburger 11
Sushi
5
Don’t eat
2
• The interval is decided
by your scale.
• In this case your scale
would be from 2 – 22
and you want the scale
to fit the graph.
• The best interval
would be to go by 5’s.
TAILS
Teachers favorite food
T - Title
TAILS
Teachers’s Favorite food
T - Title
A - Axis
Y Axis =
Dependent
Variable
X Axis =
Independent
Variable
TAILS
Teachers’s Favorite food
The amount of space between
one number and the next or
one type of data and the next
on the graph.
The interval is just as important
as the scale
Choose an interval that lets you
make the graph as large as
possible for your paper and
data
T – Title
A – Axis
I – Interval
S – Scale
TAILS
Teachers’s Favorite food
25
T – Title
20
15
A – Axis
10
5
I – Interval
0
S – Scale
TAILS
Teachers’s Favorite food
LABEL your bars or
data points
Label your Y Axis. What do those
numbers mean?
T – Title
25
Number of Teachers
20
A – Axis
15
10
I – Interval
5
0
L – Labels
Singers
Give the bars a general label.
What do those words mean?
S – Scale
9/16
speed vs position at 2 holes
90
80
70
Speed (cm/s)
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
Position (cm)
• Predict what the speed is going to be at for 70
cm.
9/15 Complete the table in your
notebook
Animal
Distance
Time
Speed
Cheetah
75 m
3s
25 m/s
Greyhound
160 m
10 s
Gazelle
1 km
Turtle
Agenda
- Velocity discussion
- Acceleration discussion
- Acceleration practice
100 km / h
30 s
1 cm /s
4.2 Speed
4.4 Acceleration
We can change the state of motion of an object by changing its
speed, its direction of motion, or both.
Acceleration is the rate at which the velocity is changing.
4.4 Acceleration
A car is accelerating whenever there is a change in its state of
motion.
4.4 Acceleration
A car is accelerating whenever there is a change in its state of
motion.
4.4 Acceleration
Speed and velocity are measured in units of distance per time.
Acceleration is the change in velocity (or speed) per time
interval.
Acceleration units are speed per time.
Changing speed, without changing direction, from 0 km/h to 10
km/h in 1 second, acceleration along a straight line is
4.4 Acceleration
A car is accelerating whenever there is a change in its state of
motion.
4.4 Acceleration
Accelerate in the direction of velocity–speed up
Accelerate against velocity–slow down
Accelerate at an angle to velocity–change direction
4.4 Acceleration
think!
Suppose a car moving in a straight line steadily increases its
speed each second, first from 35 to 40 km/h, then from 40 to 45
km/h, then from 45 to 50 km/h. What is its acceleration?
In other words the car speeds up from 35 km/h to 50 km/h in 3
seconds. What is the acceleration?
4.1 Acceleration
• Acceleration is the rate of change in the speed of an
object.
• Rate of change means the ratio of the amount of change
divided by how much time the change takes.
4.1 Acceleration in metric units
• If a car’s speed increases from
8.9 m/s to 27 m/s, the
acceleration in metric units is
18.1 m/s divided by 4 seconds,
or 4.5 meters per second per
second.
• Meters per second per second
is usually written as meters per
second squared (m/s2).
4.1 The difference between velocity
and acceleration
• Velocity is fundamentally different from
acceleration.
• Velocity can be positive or negative and is the
rate at which an object’s position changes.
• Acceleration is the rate at which velocity
changes.
Inv 4.1 Acceleration
Investigation Key Question:
How does acceleration relate to velocity?
4.1 The difference between velocity
and acceleration
• The acceleration of an
object can be in the
same direction as its
velocity or in the
opposite direction.
• Velocity increases when
acceleration is in the
same direction.
4.1 Calculating acceleration
• The formula for acceleration can also be written
in a form that is convenient for experiments.
4.1 Calculating acceleration
• Acceleration is the change in velocity divided by
the change in time. The Greek letter delta (Δ)
means “the change in.”
Acceleration
(m/sec2)
a = Dv
Dt
Change in speed (m/sec)
Change in time (sec)
9/16
speed vs position at 8 cm
90
80
70
Speed (cm/s)
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
Position (cm)
• Predict what the speed is going to be at for 70
cm.
Find the initial velocity through the first photogate in cm/s. Remember the
distance of the flag is one cm
initial velocity 1 cm/.01373 s = 72.83 cm / s
Find the final velocity through the second photogate?
Final velocity is 1/ (.36240-.35680)= 178.57
How could use photogates to measure time on the track?
Final time – initial time = .35680 - .0000 = .35680 s
• How could you find acceleration
• Vf – Vi / T
Change in velocity (178.57 cm/s – 72.83 cm /s )
= 105.74 cm/s
Acceleration 105.74/ .3568 = 296.35 cm/s/s
Calculating acceleration in m/s2
A student conducts an acceleration experiment
by coasting a bicycle down a steep hill. A partner
records the speed of the bicycle every second for
five seconds. Calculate the acceleration of the
bicycle.
1.
2.
3.
4.
–
–
You are asked for acceleration.
You are given times and speeds from an
experiment.
Use the relationship
a = (v2 – v1) ÷ (t2 – t1)
Choose any two pairs of time and speed data
since the change in speed is constant.
a = (6 m/s 4 m/s) ÷ (3 s – 4 s) = (2 m/s) ÷ (-1 s)
a = −2 m/s
4.1 Constant negative acceleration
• Consider a ball rolling up a
ramp.
• As the ball slows down,
eventually its speed becomes
zero and at that moment the
ball is at rest.
• However, the ball is still
accelerating because its
velocity continues to change.
• http://www.glencoe.com/sec/science/inter
net_lab/images/physicsCh1.mov
Fill out the following table
Time
Accelerat
ion
V final
V average
Distance
traveled
0
10 m/s/s
0 m/s
0 m/s
0m
1
10 m/s/s
10 m/s
5 m/s
5m
2
10 m/s/s
3
10 m/s/s
4
10 m/s/s
5
10 m/s/s
• Challenge : try to find a formula for time
9/4
• 1. What is the difference between
speed and velocity?
• 2. If you are traveling at 60 mph how
long would it take you to travel 180
miles? Show your work.
• Agenda : Aces high
9/8
• What were the main differences between a
fast flier and a slow flier?
• What are some modifications you made?
Due today :
* Lab report on paper planes
The summary should include discussion
on how your followed the enginnering
and design process
•
•
•
•
•
What sort of data could you take
Time
Distance speed
Dimensions of your plane
How do you measure speed?
Concept check
1. You are running at 5 m/s towards a wall
that is 10 meters away, how long before you
hit it?
2. You are running at the same wall at 2 m/s
and you hit it 5 seconds later how far away is
the wall?
• http://phet.colorado.edu/en/simulation/m
oving-man
• What is the relationship between time and
velocity?
4.4 Acceleration
think!
Suppose a car moving in a straight line steadily increases its
speed each second, first from 35 to 40 km/h, then from 40 to 45
km/h, then from 45 to 50 km/h. What is its acceleration?
Answer: The speed increases by 5 km/h during each 1-s interval
in a straight line. The acceleration is therefore
5 km/h•s during each interval.
4.4 Acceleration
think!
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?
4.4 Acceleration
think!
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?
Answer: The car and truck both increase their speed by
15 km/h during the same time interval, so their acceleration is
the same.
4.5 Free Fall: How Fast
Falling Objects
Imagine there is no air resistance and that
gravity is the only thing affecting a falling
object.
An object moving under the influence of
the gravitational force only is said to
be in free fall.
The elapsed time is the time that has
elapsed, or passed, since the
beginning of any motion, in this case
the fall.
• On Jupiter, A ball starts at 5 m/s and travels
down a ramp and gains a speed of 35 m/s in
3 seconds. What is the balls acceleration?
• Light travels in a straight line at a constant
speed of 300,000 km/s, what is the lights
acceleration?
• Create a bubble map around the word flight
What is engineering
• http://www.discoverengineering.org/
•
•
•
•
•
•
Types of engineering
Nuclear
Medical
Mechanical
Chemical
Electrical
Engineering and design process
•
•
•
•
•
•
•
•
1. Identify the problem
2. Identify criteria and constraints
3. Brainstorm possible solutions
4. Generate ideas
5. Explore possibilities
6. Select an approach
7. build a model
Refine the design
• What do you need in order to finish your lab
report?
http://science360.gov/obj/tkn-video/fc729ef022ee-4f61-bb2a-b6c07685fb02/science-nflfootball-projectile-motion-parabolas
Perigrine falcon dive
http://www.youtube.com/watch?v=legzXQlF
Njs
http://www.youtube.com/watch?v=IyFofv8Zq
dE&feature=related
Early flight
http://www.youtube.com/watch?v=iMhdksPFhC
M
2/18
Turn in plane lab
1. Who will win a 20 meter race some one who is
running at a constant 2 m/s or some one who is
starting from 0 but has an acceleration at 1 m/s.
• Draw two number lines and represent each
runner graphically after each second. (see
handout)
• 2. Try again with a runner that is traveling at a
constant 3 m/s
The Cheetah: A cat that is built for speed. Its strength and agility
allow it to sustain a top speed of over 100 km/h. Such speeds can
only be maintained for about ten seconds.
Photo © Vol. 44 Photo Disk/Getty
Objectives: After completing this
module, you should be able to:
• Define and apply concepts of average and
instantaneous velocity and acceleration.
• Solve problems involving initial and final velocity,
acceleration, displacement, and time.
• Demonstrate your understanding of directions and
signs for velocity, displacement, and acceleration.
• Solve problems involving a free-falling body in a
gravitational field.
Uniform Acceleration
in One Dimension:
• Motion is along a straight line (horizontal,
vertical or slanted).
• Changes in motion result from a CONSTANT
force producing uniform acceleration.
• The cause of motion will be discussed later. Here
we only treat the changes.
• The moving object is treated as though it were a
point particle.
Distance and Displacement
Distance is the length of the actual path taken
by an object. Consider travel from point A to
point B in diagram below:
Distance s is a scalar quantity (no
direction):
s = 20 m
A
B
Contains magnitude only and consists of a
number and a unit.
(20 m, 40 mi/h, 10 gal)
Distance and Displacement
Displacement is the straight-line separation of
two points in a specified direction.
D = 12 m, 20o
A
q
B
A vector quantity:
Contains magnitude AND
direction, a number, unit
& angle.
(12 m, 300; 8 km/h, N)
Distance and Displacement
• For motion along x or y axis, the displacement is
determined by the x or y coordinate of its final position.
Example: Consider a car that travels 8 m, E then 12 m, W.
Net displacement D is from the origin
to the final position:
D
D = 4 m, W
What is the distance
traveled? 20 m !!
8 m,E
x = -4
x = +8
12 m,W
x
The Signs of Displacement
• Displacement is positive (+) or negative
(-) based on LOCATION.
Examples:
The displacement is
the y-coordinate.
Whether motion is up
or down, + or - is based
on LOCATION.
2m
-1 m
-2 m
The direction of motion does not matter!
Definition of Speed
• Speed is the distance traveled per unit of
time (a scalar quantity).
s = 20 m
A
Time t = 4 s
B
v=
s
t=
20 m
4s
v = 5 m/s
Not direction dependent!
Definition of Velocity
• Velocity is the displacement per unit
of time. (A vector quantity.)
s = 20 m
D=12 m
B
D 12 m
v 
t
4s
A
20o
Time t = 4 s
v = 3 m/s at 200 N of E
Direction required!
Example 1. A runner runs 200 m, east, then changes
direction and runs 300 m, west. If the entire trip takes 60
s, what is the average speed and what is the average
velocity?
Recall that average speed is a
function only of total distance and
total time:
s2 = 300 m
s1 = 200 m
start
Total distance: s = 200 m + 300 m = 500 m
total path 500 m
Average speed 

time
60 s
Direction does not matter!
Avg. speed 8.33 m/s
Example 1 (Cont.) Now we find the average velocity,
which is the net displacement divided by time. In this
case, the direction matters.
v
x f  x0
t = 60 s
xf = -100 m
x1= +200 m
t
xo = 0
x0 = 0 m; xf = -100 m
100 m  0
v
 1.67 m/s
60 s
Average velocity:
Direction of final displacement is to
the left as shown.
v  1.67 m/s, West
Note: Average velocity is directed to the west.
Example 2. A sky diver jumps and falls for 600 m in 14
s. After chute opens, he falls another 400 m in 150 s.
What is average speed for entire fall?
14 s
Total distance/ total time:
x A  xB 600 m + 400 m
v

t A  tB
14 s + 150 s
1000 m
v
164 s
v  6.10 m/s
Average speed is a function only of total distance
traveled and the total time required.
A
625 m
B
356 m
142 s
Examples of Speed
Orbit
2 x 104 m/s
Light = 3 x 108 m/s
Jets = 300 m/s
Car = 25 m/s
Speed Examples (Cont.)
Runner = 10 m/s
Glacier = 1 x 10-5 m/s
Snail = 0.001 m/s
Average Speed and Instantaneous
Velocity
 The average speed depends ONLY on the
distance traveled and the time required.
A
s = 20 m
C
Time t = 4 s
B
The instantaneous
velocity is the magnitude and direction of
the speed at a particular instant. (v at
point C)
The Signs of Velocity
 Velocity is positive (+) or negative (-)
based on direction of motion.
+
+
-
+
First choose + direction; then
v is positive if motion is with
that direction, and negative if
it is against that direction.
2/19
• Is a track athlete more likely to report their velocity or
speed? Is it more likely to be an average or
instantaneous.
• The speed of sound is about 340 meters per second. If
you shout h-el-l-o and hear your voice 2.4 seconds
later, how far are you from the cliff wall?
• Agenda: Warm up
• moving man exercise
• finish practice problems
• http://phet.colorado.edu/en/simulation/moving-man
• Record three patterns you noticed in the graphs
2/20
• 1. Draw a quick representation of a particle
going in constant motion and one going in
accelerated motion. (number line or x/y
cartesian graph).
2/23
1. What is one thing you are going to investigate.
2. You walk up to the wall slowly for 3 seconds, stop
for 2 seconds then back up quickly for one second
to your original spot. Create the following graphs of
this situation.
a. Position vs. time
b. Velocity vs. time
c. Acceleration vs. time
• Present at end of hour.
• Create a claim evidence and reasoning sheet.
and share out one thing your group has
discovered.
• Claim : What did you find out?
• Evidence : What did your graphs show? Draw
pictures of your graphs
9/21
1. Who will win a 20 meter race some one who is running at a constant 2 m/s or some
one who is starting from 0 but has an acceleration at 1 m/s.
• Draw two number lines and represent each runner graphically after each second.
(see handout)
Try again with a runner that is traveling at a constant 3 m/s
2. Usain Bolt broke the world’s record when he ran the 100 meter in under 10
seconds. What was his speed in m/s.
•
https://www.youtube.com/watch?v=QSYObch2nNI
1. Create a velocity time graph of what you think
this looks like. (remember to label)
2. Do the same for a distance time graph.
3. An acceleration time graph.
4. Now add a cheetah to your graphs
https://www.youtube.com/watch?v=Km2JDIR8-8I
• What causes the cheetah and the sprinter to
accelerate?
• What is the formula for acceleration?
• Acceleration -practice
• A soccer player ran west down the field for 80
meters then back east for 40 meters. It took
her 20 seconds.
• What is the average velocity?
Average and Instantaneous v
Average Velocity:
vavg
Instantaneous Velocity:
Dx x2  x1


Dt t2  t1
vinst
Dx

(Dt  0)
Dt
x2
Dx
x1
Dt
t1
t2
Displacement, x
slope
Dx
Dt
Time
Definition of Acceleration
 An acceleration is the change in velocity
per unit of time. (A vector quantity.)
 A change in velocity requires the
application of a push or pull (force).
A formal treatment of force and acceleration will be given later. For now, you should
know that:
• The direction of acceleration is same as
direction of force.
• The acceleration is
proportional to the
magnitude of the force.
Acceleration and Force
F
a
2F
2a
Pulling the wagon with twice the force
produces twice the acceleration and
acceleration is in direction of force.
Example of Acceleration
+
Force
t=3s
v0 = +2 m/s
vf = +8 m/s
The wind changes the speed of a boat
from 2 m/s to 8 m/s in 3 s. Each second
the speed changes by 2 m/s.
Wind force is constant, thus acceleration is constant.
The Signs of Acceleration
• Acceleration is positive (+) or negative (-)
based on the direction of force.
+
F
a (-)
F
a(+)
Choose + direction first.
Then acceleration a will
have the same sign as that
of the force F —regardless
of the direction of velocity.
Average and Instantaneous a
aavg
Dv v2  v1


Dt t2  t1
ainst
Dv

(Dt  0)
Dt
slope
v2
Dv
Dv
v1
Dt
Dt
t1
t2
time
Example 3 (No change in direction): A constant force
changes the speed of a car from 8 m/s to 20 m/s in 4 s.
What is average acceleration?
+
Force
t=4s
v1 = +8 m/s
Step 1. Draw a rough sketch.
Step 2. Choose a positive direction (right).
Step 3. Label given info with + and - signs.
Step 4. Indicate direction of force F.
v2 = +20 m/s
Example 3 (Continued): What is average
acceleration of car?
+
Force
t=4s
v1 = +8 m/s
Step 5. Recall definition of average
acceleration.
aavg
Dv v2  v1


Dt t2  t1
v2 = +20 m/s
20 m/s - 8 m/s
a
 3 m/s
4s
a  3 m/s, rightward
Example 4: A wagon moving east at 20 m/s
encounters a very strong head-wind, causing it to
change directions. After 5 s, it is traveling west at 5
m/s. What is the average acceleration? (Be careful
of signs.)
+
Force
E
vf = -5 m/s
vo = +20 m/s
Step 1. Draw a rough sketch.
Step 2. Choose the eastward direction as positive.
Step 3. Label given info with + and - signs.
Example 4 (Cont.): Wagon moving east at 20 m/s
encounters a head-wind, causing it to change
directions. Five seconds later, it is traveling west at 5
m/s. What is the average acceleration?
Choose the eastward direction as positive.
Initial velocity, vo = +20 m/s, east (+)
Final velocity, vf = -5 m/s, west (-)
The change in velocity, Dv = vf - v0
Dv = (-5 m/s) - (+20 m/s) = -25 m/s
Example 4: (Continued)
+
Force
E
vf = -5 m/s
Dv
aavg = Dt=
vo = +20 m/s
Dv = (-5 m/s) - (+20 m/s) = -25 m/s
vf - vo
tf - to
a = - 5 m/s2
-25 m/s
a=
5s
Acceleration is directed to left, west (same as
F).
Signs for Displacement
+
Force
C
D
E
A
vf = -5 m/s
vo = +20 m/s
a = - 5 m/s2
Time t = 0 at point A. What are the signs
(+ or -) of displacement at B, C, and D?
At B, x is positive, right of origin
At C, x is positive, right of origin
At D, x is negative, left of origin
B
Signs for Acceleration
+
C
D
A
vf = -5 m/s
vo = +20 m/s
What are the signs (+ or -) of acceleration at
Force
E
B
a = - 5 m/s2
points B, C,
and D?
 At B, C, and D, a = -5 m/s, negative
at all points.
 The force is constant and always directed
to left, so acceleration does not change.
Definitions
Average velocity:
vavg
Dx x2  x1


Dt t2  t1
Average acceleration:
aavg
Dv v2  v1


Dt t2  t1
Velocity for constant a
Average velocity:
vavg
Average velocity:
Dx x f  x0


Dt t f  t 0
vavg 
v0  v f
Setting to = 0 and combining we have:
x  x0 
v0  v f
2
t
2
2/25
• Objects that are freefalling have an
acceleration of 10 m/s/s. You drop a rock off a
bridge. 3 seconds later you here a splash.
• How fast was it going after 3 seconds?
• What was the average speed?
• How far did it go
4.5 Free Fall: How Fast
think!
What would the speedometer reading on the falling rock be
4.5 seconds after it drops from rest?
How about 8 seconds after it is dropped?
4.5 Free Fall: How Fast
think!
What would the speedometer reading on the falling rock be
4.5 seconds after it drops from rest?
How about 8 seconds after it is dropped?
Answer: The speedometer readings would be 45 m/s and
80 m/s, respectively.
Fill in the chart
Time (s)
Acceleration
(m/s/s)
Final velocity Average
(m/s)
velocity
(m/s)
Distance (m)
0
1
2
3
4
• What is the relationship between distance
traveled and time?
Fill in the chart
Time (s)
Acceleration
(m/s/s)
Final velocity Average
(m/s)
velocity
(m/s)
Distance (m)
0
10
0
0
0
1
10
10
5
5
2
10
20
10
20
3
10
30
15
45
4
10
40
20
80
• What is the relationship between distance
traveled and time?
Fill in the chart
Time (s)
Acceleration
(m/s/s)
Final velocity Average
(m/s)
velocity
(m/s)
Distance (m)
0
10
0
0
0
1
10
10
5
5
2
10
20
10
20
3
10
30
15
45
4
10
40
20
80
• What is the relationship between distance
traveled and time?
Fill in the chart
Time (s)
Acceleration
(m/s/s)
Final velocity Average
(m/s)
velocity
(m/s)
Distance (m)
0
10
0
0
0
1
10
10
5
5
2
10
20
10
20
3
10
30
15
45
4
10
40
20
80
• What is the relationship between distance
traveled and time?
Fill in the chart
Time (s)
Acceleration
(m/s/s)
Final velocity Average
(m/s)
velocity
(m/s)
Distance (m)
0
1
2
3
4
• What is the relationship between distance
traveled and time?
Fill in the chart
Time (s)
Acceleration
(m/s/s)
Final velocity Average
(m/s)
velocity
(m/s)
Distance (m)
0
1
2
3
4
• What is the relationship between distance
traveled and time?
Fill in the chart
Time (s)
Acceleration
(m/s/s)
Final velocity Average
(m/s)
velocity
(m/s)
Distance (m)
0
1
2
3
4
• What is the relationship between distance
traveled and time?
4.6 Free Fall: How Far
These distances form a mathematical pattern: at the end of
time t, the object starting from rest falls a distance d.
4.6 Free Fall: How Far
4.5 Free Fall: How Fast
2/26
• Is the unit of light year a speed, distance, or
time?
• Consider an object being dropped in a
vacuum (see video).
• A. Create an acceleration versus time graph
• B. a velocity versus time graph
• C. a position versus time graph
Notebook check:2/17- 2/26
Skip #10
• Brian Cox visits the world's biggest vacuum
chamber
• https://www.youtube.com/watch?v=E43CfukEgs