Transcript Average Speed

Average Speed
Mrs. Martinez
Sixth Grade
Welcoming Work
Review
 What is Force?
 What is a balanced force? Describe by using
arrows to draw a diagram.
 What is an unbalanced force? Describe by using
arrows to draw a diagram.
Getting your brain gears turning.
 What is a distance-time graph?
 What is Motion?
 What is the connection between Speed,
Distance, and Time?
Forces
A force is a push or pull
that one body exerts on
another. A force can
cause the motion of an
object to change. There
are two types of forces:
 Balanced force – one in
which the net force is
zero.
 Unbalanced force – one in
which the net force has a
numerical value.

Forces
Balanced Force
+ 1 force
- 1 force
Net force = 0
Unbalanced Force
+ 1 force
+ 1 force
- 2 force
Unbalanced Force
Net force = +2
+ 1 force
Net force = -1
Turn and Talk
What is motion?
What Is Motion?

Motion is when an object changes place or
position. To properly describe motion,
you need to use the following:
Start and end position?
 Movement relative to what?
 How far did it go?
 In what direction did it go?

Motion Re-Cap

When an object changes its position, motion has occurred.
– Distance- How far an object has moved.
– Displacement- How far an object has moved in
relation to its starting point.
– Consider direction
Example: Two runners travel along the same straight path
in a straight line for 500 meters. At the end of the run
their distances are the same but their displacements are
different. How can this be so?
SPEED
Describes how fast an object
is moving.
What Is Speed?
Speed is the distance an
object travels in a certain
amount of time
 To calculate speed, you
use the following formula:
Speed (s) =Distance(d)
Time (t)

(relationship of all 3)
Speed- Distance an object travels per
unit of time
Relationships between speed, distance,
and time:
Speed = Distance/ Time = d/ t
 Constant Speed- speed does not
change over time
 Average Speed- speed of motion when
speed is changing
Avg Speed = Total Distance/ Total Time
 Instantaneous Speed- speed at any
given moment in time (speedometer)
The 3 formulas for Speed, Time & Distance:
Using your W/B write them down without using your notes
Distance
Speed =
Time
Solving for Speed
Time =
Distance
Speed
Solving for Time
.
Distance = Speed x Time
Solving for Distance
D
Remember them from
this triangle:
S
T
http://www.youtube.com/watch?v=9x7hP5LM1UE
DON’T REMEMBER HUH?
WELL LET’S REFRESH THAT
MEMORY!
Turn and Talk: What is the
Relationship between speed,
distance and time?

Speed is the distance an object travels in
a certain amount of time
Average Speed =
Total distance
Total time
WB Time!
Let’s check out your knowledge! Without
using your notes answer:
 What is the formula for finding speed?


What is the formula for finding time, using
distance and speed?

What is the formula for finding distance
using speed and time?
Try this

Mrs. Martinez walks home from her sister’s
house everyday. It takes her 4 minutes
and her house is 240 meters away.What is
her average speed?

240 meters/ 4 minutes =

60 meters per minute.
Example Question 1

Jane drives at an average speed of 45
mph on a journey of 135 miles.
How long does the journey take?

To find a time, we need to divide distance
by speed.

135 miles ÷ 45 mph = 3 hours
Example Question 2

Chris cycles at an average speed of 8
mph.
If he cycles for 6½ hours, how far does
he travel?

To find a distance, we need to multiply
speed by time.

8 mph × 6.5 hours = 52 miles
Example Question 3

Nikki has to travel a total of 351 miles.
She travels the first 216 miles in 4 hours.
(a) What is her average speed for the first
part of the journey?

To find average speed, we need to divide
distance by time.

216 miles ÷ 4 hours = 54 mph

Her average speed is the same for the
whole of her journey.

(b) How long does the whole journey
take?

To find time, we need to divide distance
by speed.
 351 miles ÷ 54 mph = 6.5 hours
Reminder: How to change minutes into a decimal
15 mins = 0•25 hour
So: 3 hours 15 mins = 3•25 hours
30 mins = 0•5 hour
So: 7 hours 30 mins = 7•5 hours
45 mins = 0•75 hour
So: 2 hours 45 mins = 2•75 hours
First work it out on your paper then show me on your WB.
A windsurfer travelled 28 km in 1 hour 45 mins.
Calculate his speed.
Speed =
=
Distance
Time
28 km
1•75 h
D
S
T
1 hour 45 mins
= 16 km/h
Answer: His speed was 16 km / hour
A salesman travelled at an average speed of 50 km/h for
2 hours 30 mins. How far did he travel?
Distance = Speed x Time
= 50 x 2•5
D
S
T
2 hour 30 mins
= 125 km
Answer: He travelled 125 km
A train travelled 555 miles at an average speed
of 60 mph. How long did the journey take?
Distance
Time =
Speed
D
S
=
555
60
=
9•25 hours = 9 hours 15 mins
T
Answer: It took 9 hours 15 minutes
Speed Problem

Suppose you ran 2 km in
10 min. What is your
speed?
S = 2 km = 0.2 km/min

10 min

Ways To Calculate Speed



Constant speed is when you
are traveling at the same rate
of speed, such as 55 mph
constantly on a highway.
Average speed is taking the
total distance traveled, and
dividing by the total time it
takes. Used for calculations
that involve changing speed.
Instantaneous speed is the
speed at any one given point
in time.
Sooo… What is the
formula for speed?
http://www.youtube.com/watch?f
eature=endscreen&v=K_kzgW_O
YX0&NR=1
Practice Question 1

Jim travels 45 miles at 15 mph.
How long does it take him?

45 miles/15 mph=

3 hrs.
Practice Question 2

Jemimah walks at 4 mph for 2½ hours.
How far does she walk?
She walked 10 miles.
 4 mph x 2.5 hrs= 10 miles

Practice Question 3

Jenny drives at a constant speed. In the
first three hours she travels 81 miles.
How far will she have travelled after 5
hours?
She will travel 135 miles
 27 mph for 5 hrs= 135 miles

GRAPHING AVERAGE SPEED
Using a Distance-Time Graph
Graphing Motion
 Graph
distance
on the yaxis and
time on
the x-axis
Slope = rise = distance = speed
run
time
Graphing Speed
Speed is usually
graphed using a line
graph, and it depicts
the distance and time.
 Time is the independent
variable, and thus is
ALWAYS on the x-axis.
 Distance is the
dependent variable, and
is ALWAYS on the yaxis.

Bass Boat Speed
70
65
65
65
Distance (meters)
60
50
50
45
40
30
20
20
15
10
0
0
1
0
2
3
4
5
6
Time (seconds)
7
8
9
10
Average Speed
Bass Boat Speed
140
Distance (meters)
What is the
AVERAGE
speed of the
bass boat
depicted in
the graph?
125
120
100
100
85
80
65
60
65
65
50
40
20
20
0
0
1
2
3
4
5
6
7
8
9
Time (seconds)
Average Speed = 125 meters = 15.6 m/s
8 seconds
10
Instantaneous Speed
Bass Boat Speed
140
125
Distance (meters)
120
100
What is the
instantaneous
speed of the
bass boat at
t=7 seconds?
100
85
80
65
60
65
65
50
40
20
20
0
0
1
2
3
4
5
6
7
8
9
10
Time (seconds)
Instantaneous Speed = 85 meters = 12.1 m/s
7 seconds
Speed Graphs
Bass Boat Speed
70
65
65
65
Distance (meters)
60
50
50
45
40
30
20
20
15
10
0
0
1
0
2
3
4
5
6
7
8
Time (seconds)
•In what time period is the bass boat speeding up?
•In what time period is the bass boat slowing down?
•When is the speed NOT changing?
9
10
Distance - Time Graph
If something is not
moving, a
horizontal line is
drawn.
 If something starts
out slow and then
speeds up, its
change in speed
can look like this.

Learning Checkpoint
This graph shows several
stages of motion:
•Stage 1: 100 m in 10 s
•Stage 2: 50 m in 10 s
•Stage 3: 150 m in 20 s
Calculate the speed as indicated by
each of the colors.
Calculate the average speed.
What is the total distance?
What is the displacement?
Solution
Stage 1: S= d/ t
100 m/ 10 s= 10 m/s
Stage 2: S= d/t
50 m/ 10 s= 5 m/s
Stage 3: S= d/t
150 m/ 20 s= 7.5 m/s
Avg Speed= Tot d/ Tot t
300 m/ 40 s= 7.5 m/s
Distance = 300 meters
Displacement = 0 meters
3) At a daily basis, you rotate between classes. Draw a
distance vs time graph illustrating the distance you travel
during class rotations here at school
Video Recap

http://www.youtube.com/watch?v=Spz8W
fmREDM&NR=1&feature=fvwp
Average Speed Recap

http://www.youtube.com/watch?v=WxCg
VNqfub8
Velocity
The speed of an object in a certain
direction.
Velocity

Velocity is the speed of an object, but the
direction is also included. It is calculated the
same as speed, but you must include a direction
in your answer.

Example: the bass boat was moving 12 mph
toward the north.
Velocity
d
V= t
speed of an object in a certain
direction.
V = velocity (meters/second)
d = distance (meters)
t = time (seconds)
Velocity
speed of an object in a certain
direction.
0
3 seconds 1
2
Velocity
speed and direction of an
object’s motion.
–88 km / hr southwest
 The
Speed=?
Velocity=?
Total time=
4 seconds
12 meters
20 meters
16 meters
Acceleration
Acceleration is
the rate of
change of
velocity. A
change in velocity
can be either a
change in speed,
or direction, or
both.
 Deceleration is

Acceleration

The formula for calculating acceleration is:

Acceleration (a) = final velocity (vf) – initial velocity (vi)
time (sec)



The unit for velocity, in this case, is
m/s/s
OR
m/s2
Acceleration Math Problem

A jet starts at rest at the end of
a runway and reaches a speed
of 80 m/s in 20 s. What is its
acceleration?

a = 80 m/s - 0 m/s = 4
m/s2
Acceleration Math Problem



A skateboarder is moving in a straight line
at a speed of 3 m/s and comes to a stop
in 2 sec. What is his acceleration?
a = 0 m/s - 3 m/s = -1.5 m/s2
2 m/s
Inertia
Inertia is the tendency
of an object to resist
any change in motion.
Put in another way, if
an object is moving, it
will keep moving until
an outside force acts
on it.
 Inertia is related to
mass: the greater the
mass of an object, the
greater its inertia.

Newton’s 1st Law of Motion

Newton’s 1st Law is also
known as the law of inertia.
It says:

An object in motion will stay
in motion, and an object at
rest will stay at rest, unless
acted upon by an outside
force.

Example: if you are
approaching a fence on a
running horse, and the horse
Inertia
What does a seat belt do for us,
 in terms of inertia?


-it helps us OVERCOME inertia!
http://www.cimt.plymouth.ac.uk/projects/
mepres/book8/bk8i18/bk8_18i2.htm
http://baldragon.ea.dundeecity.sch.uk/Dep
artments/Physics/Movementint1/Averagesp
eedweb.htm