Do Now: ( 8 min)
A man travels from New York to Los
Angeles, a 3000 mile trip. He then travels
to Las Vegas, which is 200 miles back
towards New York. He takes a non-stop
flight to LA which takes 5 hours. His flight
to Vegas takes 1 hour.
1. What is his average speed?
2. What is his average velocity?
Review
Distance: A scalar quantity equal
to the length of one or many
displacement vector (How far
something moves)
Displacement: The vector
quantity defining distance and
direction between two positions
(How far something is from a
starting position)
Objective:
To apply what we know about scalar and vector
quantities of motion to formulas about motion in
order to prepare for a lab.
To become familiar with the proper notation
used to describe and explore motion.
Starting position: di
Final position: df
Displacement: Dd
= df - di
Time
Interval
Time interval: (Dt)
time elapsed or
taken
Average
Speed
The ratio of the
total distance
traveled over the
total time
interval
Average
Velocity (v)
The ratio of the
total
displacement
over the total
time interval
v = Dd/Dt
v = df - di
tf - ti
Instantaneous
Velocity
Instantaneous
velocity:the
speed & direction
at a particular
instant
Example #1: Time
Interval
A car begins traveling to New
York at 3:00 and arrives at 6:30.
What was the time it took to
travel?
6:30-3:00 = 3.5 h
Example #2: Average
Speed
A car starts traveling North to
New York which is 200 miles away
in 4 hours. What was its average
speed?
200/4 = 50 mph
Example #3: Average
Velocity
A car traveled 200 mi North from
Baltimore to New York in 4 hours.
What was its average velocity?
200mi/4 h = 50 mph North
Example #4:
Instantaneous Velocity
A car begins traveling North at
3:00 at 60 mph. It speeds up by 10
mph at 4:00. What was its
instantaneous velocity at 4:00?
60+10 = 70 mph North
at 4:00
Acceleration
Acceleration: The
change in velocity
per unit time
Units: v/t = (m/s)/s =
2
m/(s X s) = m/s
otherwise stated in the problem)
(unless
Average
Acceleration
a = Dv/Dt
a = vf - vi
tf - ti
Example #5
A car goes from, 0 – 60 m/s in 5
s. What is its acceleration?
(60m/s-0m/s)/5s = 12 m/s2
Example #6
An airplane takes off from rest
and reaches a speed of 400 m/s
in 10 s. What is its acceleration?
(400m/s-0m/s)/10s = 40 m/s^2
Practice
Begin working on your homework. It
is due Wednesday September 28
Do Now (9/27): (4 min)
A NASA rocket blasts off
from 0 m/s to 500 m/s in 12 s.
What is its acceleration?
Reminders:
When solving problems, you must show
all work for credit!!! This means:
Listing variables: d= 3m, t=4s, s=?
showing a formula: s=d/t
plugging in: s = 3m/4s
boxing your answer with the correct
notation and units
S = .75 m/s
When solving word problems, look for
context clues to tell you what you’re
solving for
Distance ( measured in m):
How far something went
How high/large/small something is
Where something is or moved to
Time (measured in s):
How long it took
How much time passed
Velocity/speed: (measured in m/s)
The rate of an object
How fast something traveled
Acceleration (measured in m/s2):
How fast something sped up
How fast something slowed down
Mini Quiz:
If a Ferrari, with an initial
velocity of 10 m/s,
accelerates at a rate of
2
50 m/s for 3 seconds,
what will its final velocity
be?
Do Now (9/28):
If a car accelerates to a
velocity of 60 m/s, at a
2
rate of 50 m/s for 4
seconds, what was its
initial velocity?
Objective:
To use what we know about displacement, time
velocity, and acceleration to graph different
types of motion
To practice making graphs to prepare for a lab
on motion
Distance/Position vs. Time Graphs
Example: You went for a walk to the near by store (10 km north)
and back to your original reference point. This would mean your
total travelled distance is 20 km (10km to the store, and 10km
back). This distance-time graph would look like the following:
What’s the difference? Discuss!
Position-time graphs
Position graphs
depend on direction
(remember
displacement, which is
the change in position,
is a vector quantity)
Graphing Position-Time Graphs
•Time is always the I.V. (x-axis)
•Position is always the D.V. (y-axis)
Is this graph
linear?
Example:
Time (t) measured in s
Position (x) measured in cm
0.1
20
0.2
40
0.3
60
0.4
80
•∆x= change in
position (aka
displacement);
displacement can
be represented by
any variable that
represents
position (x, y, d,
etc.)
•∆t= change in time
Finding the average velocity
Draw a line of best fit and find the
slope
rise Dx
slope 

 velocity!!!!
run Dt
What is the
slope of this
line?
Practice:
Directions:
1. Work with a partner. Have one partner get a whiteboard
and dry erase marker.
2. Create the graph on the board in the time provided.
3. Draw a line of best fit and find the velocity (slope).
4. Present your graph when finished.
Time (t) measured in s
Position (x) measured in m
5
11
10
20
15
29
20
42
25
51
30
58
35
70
40
79
Example #1:
Practice:
Directions:
1. Work with a partner. Have one partner get a whiteboard
and dry erase marker.
2. Create the graph on the board in the time provided.
3. Draw a line of best fit and find the velocity (slope).
4. Present your graph when finished.
Example #2:
Time (t) measured in s
Position (x) measured in m
70
200
80
180
90
159
100
132
110
118
120
104
130
89
140
73
Graphing
Data
st
1
Order: y = 2x
t 0 1 2 3 4 5
d 0 2 4 6 8 10
1st Order Curve
5
4
3
2
1
0
0
1
2
3
4
5
nd
2
Order Curve Y =
t 0
d 0
1
1
2
4
2
x
3 4 5
9 16 25
2nd Order Curve
25
20
15
10
5
0
0
1
2
3
4
5
rd
3
t 0
d 0
Order Curve
1
1
2 3 4 5
8 27 64 125
y=
3
x
3rd Order Curve
130
110
90
70
50
30
10
-10
0
1
2
3
4
5
Velocity/Time Graphs
•v/t graphs are identical to p/t graphs except that
velocity is graphed on the y-axis instead of
position.
•The slope of a v/t graph is… acceleration!
Dv
a
Dt
Practice:
Directions:
1. Work with a partner. Have one partner get a whiteboard and
dry erase marker.
2. Create the graph on the board in the time provided.
3. Draw a line of best fit and find the velocity (slope).
4. Present your graph when finished
Constant Speed p/t graph
•The motion is linear
•Rate of change is constant – the position increases by
the same amount for every time interval
•This means the slope (which represents the velocity)
is constant
Changing Speed p/t graph
•The motion is non-linear
•Rate of change is changing– the position increases by
a different amount for every time interval
•This means the slope (which represents the velocity)
is changing
•Changing
velocity
means…
acceleration!
Examples:
Constant Velocity
Positive Velocity
Positive Velocity
Changing Velocity
(acceleration)
Constant acceleration v/t graph
•For a v/t graph, slope represents
acceleration – constant slope means
constant acceleration
But what if
there’s no
acceleration?
For no acceleration, use the
following graph:
Positive Velocity
Zero Acceleration
Motion Lab Graphs
Use the remainder of the period to work on
your graphs
Remember, you need an IDEAL graph for
each of your eight graphs, as well as the
graphs of your data. Use the graphs we just
went over to create your ideal p/t and v/t
graphs for constant speed and changing
speed (acceleration) – you should have four
graphs of each
Do Now (9/29)
Describe the motion of each graph:
Do Now (9/29)
Describe the motion of each graph:
1.
3.
2.
4.