1
Speed and Velocity
What is speed, velocity and acceleration?
Speed and Velocity
(Use with Speed, Velocity and Acceleration handout)
2
Speed is the distance traveled per unit of time.
Speed (s) =
distance (d)
time (t)
Each variable measured by units:
Distance: meters (m), miles (mi)
Time:seconds (s), hours (hr), minutes (min)
Speed:
meters per second (m/s),
miles per hour (mi/hr),
kilometers per hour (km/hr)
3
3 TYPES OF SPEED
Instantaneous, Average, Constant
Pretend you are looking at your car's speedometer while you are
driving. The reading you get from your speedometer is
A. instantaneous speed…
This is the speed that you are traveling at that moment.
4
B. Constant Speed is when the object covers equal
distances in equal amounts of time.
C. Average speed is the total distance
traveled divided by the total time. It can be
calculated using the following formula:
speed =
distance
time
...or shortened:
Average Speed is:
Total distance =
distance traveled
all
over
Total time =
final time (end) minus
initial time (beginning)
5
Four Step Approach to Solving Problems
G.U.E.S.S.A.
Step 1 READ THE PROBLEM.
Draw a picture.
Step 2 IDENTIFY THE VARIABLES
Write down what you know. GIVEN
What are you trying to find? UNKNOWN
Step 3
WRITE FORMULA
EQUATION
Set up the formula.
(The formula should match the unknown.)
Step 4 PLUG IN THE NUMBERS.
SUBSTITUTE
DO THE MATH
SOLVE.
Check ANSWER with UNITS
6
Consider the problem…
“A car traveled 110 miles in 2 hours.”
Step 1
Read the problem.
Draw a picture.
110 miles
2 hours
d=
t=
s=
Formula
Plug-in
Units, units, units!
Answer
7
“A car traveled 110 miles in 2 hours.”
Step 2
Write down what you know. GIVEN
What are you trying to find? UNKNOWN
110 miles
2 hours
d = 110 miles
t = 2 hours
s=
Formula
Plug-in
Units, units, units!
Answer
8
“A car traveled 110 miles in 2 hours.”
Step 3 Set up the formula.
FORMULA SHOULD MATCH THE UNKNOWN
s=
d = 110 miles
t = 2 hours
s=
Formula
d
t
Plug-in
Units, units, units!
Answer
9
“A car traveled 110 miles in 2 hours.”
Step 3
Formula
d = 110 miles
d
t = 2 hours
S=
s=
t
Set up the formula. EQUATION
Plug-in
Units, units, units!
Answer
10
“A car traveled 110 miles in 2 hours.”
Step 4
Plug-in the numbers. SUBSTITUTE
AND SOLVE. CHECK UNITS
55 mi/hr
Formula
d = 110 mi
d
t = 2 hours
S=
s = 55 mi/hr
t
Plug-in
Answer
S = 110 mi S = 55 mi/hr
2 hr
Units, units, units!
11
Do the problems 1-3
on your notes.
12
Consider the problem…
“A runner’s average speed during the 10 kilometer race
was 20 km/hr. What was his time?’”
Step 1
Read the problem.
Draw a picture.
Speed of runner:
20 km/hr
d=
t=
s=
CIRCLE AND LABEL
INFO PROVIDED!
10 km
Formula
Plug-in
Units, units, units!
Answer
13
“A runner’s average speed during the 10 kilometer race
was 20 km/hr. What was his time?”
Step 2 Write down what you know.
What are you trying to find?
Speed of runner:
20 km/hr
d = 10 km
GIVEN
UNKNOWN
10 km
Formula
Plug-in
t=
s = 20 km/hr
Units, units, units!
Answer
14
“A runner’s average speed during the 10 kilometer race
was 20 km/hr. What was his time?’”
Step 3
Set up the formula.
FORMULA MUST MATCH UNKNOWN
t=
d = 10 km
Formula
t=
t (hr) =
s = 20 km/hr
d
s
Plug-in
d (km)
s (km/hr)
Units, units, units!
Answer
15
“A runner’s average speed during the 10 kilometer race
was 20 km/hr. What was his time?’”
Step 4 SUBSTITUTE AND SOLVE
Plug-in the numbers and do the math.
Check units for answer.
Time: 0.5 Hour
d = 10 km
t = 0.5 hr
s = 20 km/hr
Formula
t=
d
s
Plug-in
t = 10 km
(hr) 20 km/hr
Units, units, units!
Answer
10 km
=0.5
20 km/hr
hr
16
Do the problems 4-5
on your notes.
17
“You decide to go to Dallas to see friends. Your friends
tell you that it takes 4 hours to get to Dallas at an
average speed of 70 miles per hour.
hour Approximately
how many miles is it to their house?”
Step 1
Read the problem.
Draw a picture.
Step 2
Write down what you know. GIVEN
What are you trying to find? UNKNOWN
Step 3
?
Set up the formula. EQUATION
Step 4
Plug-in the numbers. SUBSTITUTE
Do the math. SOLVE. ANSWER with correct unit.
d = 280 mi
Formula
t = 4 hr
s = 70 mi/hr
d=s*t
Plug-in
Answer
d =70 mi/hr * 4 hr
= 280 mi
Units, units, units!
18
Do problem 6 on your
notes.
19
Instantaneous speed
(Reading on your speedometer)
and Average speed
distance traveled over
(Total
total time)
Both do not involve direction.
20
What is the difference
between speed and velocity?
Velocity has speed & direction.
55 mi/hr
All of these cars had
different velocities
because they were traveling in different directions.
21
A distance/time graph makes it possible to “see” speed.
This graph shows how fast the swimmers went during
their workout.
Rate of Swimmers
2400
2000
Which one stopped
during his/her workout?
1600
Distance in meters
Which swimmer swam at a
constant (the same) speed
throughout her workout?
1200
800
Stopped here
400
400 meters at 10, 15, & 20 minutes
0
0
5
10
15
Time in minutes
20
25
30
22
Make the speed graph
& answer the questions.
23
Acceleration
24
Acceleration is defined
as the change in
velocity over time.
Any time an object's velocity is
changing, we say that the object is
accelerating.
This brings up an important point. In
common language, when things
speed up, we say that they are
"accelerating," and, when they slow
down, we say that they are
"decelerating."
25
However, in the language of
physics, we say that both
objects are accelerating, not
because both objects are
speeding up, but because both
objects have changing
velocities.
•POSITIVE ACCELERATION (SPEEDING UP)
* NEGATIVE ACCELERATION (DECELERATING) SLOW DOWN
26
Acceleration is defined
as the change in
velocity over time.
(change) in velocity
acceleration =
acceleration =
time
final velocity – initial velocity
a=
time
Vf - Vi
t
27
A go-cart started from the top of a hill at 5 meters per
second. At the bottom of the hill it ended up with a speed
of 35 meters per second 6 seconds later. What was the
acceleration of the go-cart?
Step 1
Read the problem.
Draw a picture.
Vf =
Vi=
Formula
Plug-in
Answer
t=
a=
bottom
35 m/s
5 m/s
top
In 6 s
28
A go-cart started from the top of a hill at 5 meters per
second. At the bottom of the hill it ended up with a speed
of 35 meters per second 6 seconds later. What was the
acceleration of the go-cart?
Start:
Step 2
acceleration =
Write down what you know.
What are you trying to find?
final velocity – initial velocity
time
Vf = 35 m/s
Vi= 5 m/s
Formula
Plug-in
Answer
6s
t= 6s
a=
bottom
35 m/s
Finish:
final
Velocity
initial
Velocity
5 m/s
top
29
A go-cart started from the top of a hill at 5 meters per
second. At the bottom of the hill it ended up with a speed
of 35 meters per second 6 seconds later. What was the
acceleration of the go-cart?
Step 3
Initial
Velocity
Set up the formula.
5 m/s
top
Vf - Vi
t
Vf = 35 m/s
Vi= 5 m/s
t= 6s
a=
Formula
Plug-in
Answer
6s
Vf - Vi
t
bottom
35 m/s
Final
Velocity
30
A go-cart started from the top of a hill at 5 meters per
second. At the bottom of the hill it ended up with a speed
of 35 meters per second 6 seconds later. What was the
acceleration of the go-cart?
Step 4
Vf = 35 m/s
Vi= 5 m/s
t= 6s
a = 5 m/s2
Formula
Vf - Vi
t
Plug-in the numbers.
Solve.
Plug-in
35m/s – 5 m/s
6s
Answer
30 m/s
6s
= 5 m/s2
31
5 m/sec2
•
•
•
•
•
•
•
•
5
0
1
2
3
4
5
6
m/sec
sec
sec
sec
sec
sec
sec
sec
increase in speed every second.
0 m/sec
5 m/sec
10 m/sec
15 m/sec
20 m/sec
25 m/sec
30 m/sec
32
Do the problems 8-9
on your notes.
33
Velocity involves both speed and direction.
Changing velocity does not have to
necessarily involve a change in speed. It
could just involve a change in direction.
34
Think Differently About Acceleration
1. Consider a car moving at a constant speed
of 55 mph while turning in a circle.
2. The car's velocity is not constant, even
though the speed is constant.
Constant Speed
of 55 mph
3. WHY? This is because the direction of
motion is constantly changing while the car
is turning around the track.
4. Since the direction is changing, even though
the speed is not, the velocity is changing
(velocity involves both speed and
direction).
35
Think Differently About Acceleration
5. The car is accelerating because its
velocity is changing.
Constant Speed
of 55 mph
6. As a result, the car is accelerating, even
though it is neither speeding up nor
slowing down.
36
Speed of Sound
• If you shout at a wall that is 40 meters
away how long will it take before you
hear the echo of your voice. (The
speed of sound = 343 m/sec)
37
Speed of Sound
• If you shout at a wall that is 40 meters
away how long will it take before you
hear the echo of your voice. (The
speed of sound = 343 m/sec)
•V=D
343 = 80
343T = 80
T
T
343 343
T = .23 seconds
38
Speed of Sound
• A lightening bolt flashes in the distance
and 5 seconds later you hear the clash
of thunder. How far away was the
lightening? (Speed of sounds = 343
m/sec)
39
Speed of Sound
• A lightening bolt flashes in the distance
and 5 seconds later you hear the clash
of thunder. How far away was the
lightening? (Speed of sounds = 343
m/sec)
•V=D
343 = D
D = 1715 m
T
5
40
Speed of Light
• Light from the sun is traveling at a
speed of 186,000 miles/sec. It takes
light 8 minutes to reach the Earth.
Calculate the distance from the Earth to
the sun.
41
Speed of Light
• Light from the sun is traveling at a
speed of 186,000 miles/sec. It takes
light 8 minutes to reach the Earth.
Calculate the distance from the Earth to
the sun.
•V=D
186,000 = D
T
480
D = 89,280,000 miles