Notes
A. How do you know you are moving?
1. motion: an object is in motion if its distance from another object is
changing.
2. reference point: a place or object used for comparison to determine if
something is in motion.
3. relative motion:
Whether or not an object is in motion
depends upon the reference point you choose.
a. For example, imagine you are on a train sitting in a seat next to
your best friend. The train is going 70 mph. If you use your friend
as the reference point, it would appear that you are not moving.
BUT if you use the tree outside as a reference point it would
appear that you are moving 70 mph.
The woman on the train is not moving at all when
using her baby as a reference point. But she is
moving quite fast when using a stationary object
like a tree as a reference point.
b. Another example of relative motion uses velocity. Imagine you are
in a bus that is moving 30 meters per second north (using a stationary
reference point – see diagram below). You are walking 5 meters per
second North (using a stationary passenger sitting in a bus seat as a
reference point).
Stanley the stationary
reference point
5 m/s North
30 m/s North
How fast are you walking “in reference to” (compared to) the
reference point? 30 m/s (north) + 5 m/s (north) = 35 m/s north.
You appear to be moving 35 m/s to Stanley.
4. Speed:
a. If you know the distance an object travels in a certain amount of
time, you can calculate the speed of the object. BECAUSE…the
speed of an object is the distance the object travels per unit of
time.
example
S
Ever think about what the
“speed limit” means? 55 mph
means that you travel 55
miles (distance) every hour
(time).
A cyclist travels 77 miles on his
shiny red bike through the
pristine French countryside. He
began his ride at 7am , stopped
for a 30 minute water break
around 11:30am, and arrived at his
destination at 2pm (total time = 7
hrs). What was his average speed
for the trip?
b. The speed of most objects is not constant, and therefore, the
average speed is often used in place of the instantaneous speed
(the actual speed at that instant – like the speed measurements
that police officers make with “radar guns”).
Average speed = final distance – initial distance
Total time
c. velocity: the direction and speed an object travels.
1) Weather and airplanes are two examples that show how
velocity is used. For example, during a storm meteorologist
(scientists who study the weather) will report the speed and
direction of the wind (ex. 50 mph east). An air traffic
controller (a person who watches a radar and reports to
pilots where all the other planes are in order to avoid a
midair collision) will use velocity so that pilots know how fast
and in what direction the other planes are travelling. With
this information he/she can avoid a crash.
5. Graphing Speed (Distance vs. Time)
The slope is moving upward and is a straight line.
The slope is the same at all points on the graph.
This means that the speed is constant.
The distance is not changing. This means that
the object has stopped. The slope is zero.
The Slope of a Distance versus Time Graph
Slope = rise = distance = Speed
run
time
Graph of a tiny bug crawling across the table
B
C
D
Section B: has a
steeper slope. This
means slope is
higher. The slope is
the same as the
speed. A steeper
slope means a
higher speed.
A
Run
(time = 2 minutes)
Section C: There is no
slope. The speed is 0
cm/minute. The
distance is not changing
so the bug has stopped.
Section D:This “rise”
goes down and means
that the slope is
negative
(-8). The distance
decreases which means
the object is returning
to the starting point
(coming back). -8/2
makes the velocity
-4 cm/min.
Rise
(distance from
start = 2cm)
Section A: If the rise is 2 cm and the run is 2 minutes. The slope for
“section A” is 2 cm ÷ 2 minutes which equals 1 cm/min.
6. Graph tells a story! Follow the graph above as you read the story.
For the graph above you could say: “Once upon a time, Herman had a
tiny bug named Murray. He went to his kitchen table and released the
bug from his hand. Murray crawled 1 cm/min for four minutes across
the table away from Herman’s hand. Murray then moved faster for
two minutes (2cm/min). He stopped and chowed on a juicy green leaf
for 8 minutes. He then returned to Herman’s hand in 2 minutes and
they lived happily ever after.” This was based on a true story
although names have been changed to protect the identities of
those involved.
7. Acceleration is the rate at which velocity changes and refers to
increasing speed, decreasing speed, or changing direction.
8. Calculating Acceleration: use the following formula.
Acceleration = Final speed – Initial speed
Time
Example:
As a roller coaster car starts down a slope, its speed is 4 m/s. But 3
seconds later, at the bottom, its speed is 22 m/s. What is its average
acceleration?
Speed = 4 m/s
At starting point
(= 0 seconds).
Use the formula above.
Acceleration =
22 m/s - 4 m/s
3s
Acceleration = 18 m/s
3s
Acceleration = 6 m/s2
Speed = 22 m/s
After 3 seconds
9. What does “acceleration” actually mean? Use the example above of
the rollercoaster to make sense of the timeline below. The
rollercoaster’s beginning speed (“initial speed”) is 4 m/s (meters per
second). Every second that passes the speed of the coaster increases
by 4 m/s. In other words, the speed increases 4 m/s every second OR
4 meters per second per second (No, that isn’t a typo!!!).
0 seconds
4 m/s
1 second
10 m/s
2 seconds
3 seconds
16 m/s
22 m/s
The roller coaster accelerates from 4 m/s to 22 m/s in 3 seconds. Its
acceleration is 4 m/s2 or in other words 4 meters per second per second.
10. We are used to thinking of the word “acceleration meaning that we
are speeding up. Well, in the world of physics acceleration means any
change in speed or direction!
Ice rink
Sergio skates
around the rink at a
constant speed. Is
he accelerating?
Remember, he is
constantly changing
direction as he goes
around the circle.