Usain Bolt is the world’s fastest man!!!
Physics of Motion
• We will look at:
–
–
–
–
–
–
Position
Distance
Displacement
Speed
Velocity
Acceleration
• First you need to realize that motion is relative…
Motion is relative
• What is meant by saying that motion is
relative? For everyday motion, what is motion
usually relative to?
Motion is Relative
• Motion is relative to the observer’s position
and their reference point
– Sometimes called a “reference frame”
Consider the picture…
• If this man is driving at 15 mph,
how fast is his coffee cup moving?
•Does the man feel like the cup is
moving?
•Why?
Motion is relative
• An object is in motion if it changes position
relative to a stationary reference point.
Use this to establish a COORDINATE SYSTEM
•
pick an origin or 0 point
•
decide which direction is positive
Direction
• We use N, S, E, W or
left, right, up, & down
to describe the
direction of
movement.
• We can also use
POSITIVE and
NEGATIVE to describe
direction.
POSITION
A location with respect to the origin
or zero point.
Finding Position
4
miles
0
-4
-10
4
0
-6
6
miles
10
6
0
Position depends on where
you put ‘0’.
Distance and Displacement
• Distance measures the actual path
an object takes
• Displacement measures your
overall distance from the initial
position to final position in a
STRAIGHT LINE.
• DISPLACEMENT values must
include a DIRECTION!
• Which color line represents
distance?
• Displacement?
Speed vs Velocity: Scalars vs Vectors
All measured quantities can be
classified as being either a
scalar or a vector.
Scalar
Magnitude
_________ only
(size of the quantity
….a number)
Vector
Magnitude and
_________
Direction
_________
Distance vs. Displacement
• http://physics.info/displacement/
Write in your own words- what is the
difference between distance and
displacement?
• Distance-
• Displacement-
•
Use the diagram to determine the resulting
displacement and the distance traveled by the
skier during these three minutes.
Answer
• The skier covers a distance of
• (180 m + 140 m + 100 m) = 420 m and has a
displacement of 140 m, right or east.
Formula for Displacement
How did you calculate displacementwrite a formula!
∆X = Xf-Xi
Xf= final position
Xi= initial position
Remember- displacement can be positive or
negative! (ex- what if you started at “B”?)
What is the coach's resulting
displacement and distance of travel?
Answer
• The coach covers a distance of
• (35 yds + 20 yds + 40 yds) = 95 yards and has a
displacement of 55 yards, left or -55 yards.
Speed
• Describes how fast an object moves.
• We know some things move faster than
others…but how do we measure it?
• What two quantities must you know to
determine speed?
What two quantities must you know to
determine speed?
• Choose from: displacement, distance, time,
velocity
– Hint…what is speed measured in???
– Speed= distance/time
• Ex- miles/hour, m/s, etc.
There are three types of speed you
must know…
• Constant speed
• Average speed
• Instantaneous speed
Constant Speed
• When an object covers equal distances in
equal amounts of time
• Ex- if a race car travels at a CONSTANT SPEED
of 96m/s, it will travel a DISTANCE of 96
meters EVERY SECOND.
But most objects do not travel at a
constant speed.
• The speed of an object can change from one minute
to another.
• So we can use AVERAGE SPEED to describe its
motion.
• Use this equation…
Average Speed = total Distance / total Time
Let’s try it
• A runner finished a 3 mile race in 22 minutes.
He may not have run at the same pace the
whole time, but you can still calculate his
AVERAGE SPEED
• 3 miles/22 minutes=.14 miles/min
PACE:
• 22 minutes / 3 miles = 7.33 min/mile
Instantaneous vs. Average speed
• Average speed- overall distance over time the
object traveled
• Instantaneous speed- measures speed over
small time interval (at an instant)
• Does a speedometer of a car read
instantaneous or average speed?
• What 2 controls on a car enable a change in
speed?
What if I want to describe speed AND
direction?
• For example…what if you wanted to find a
plane. Knowing the speed would only tell you
how far away to look but not in what
direction. For that we need…
• VELOCITY- the speed and direction of motion.
Let’s get back to the car example…
• Name another control that enables a change
in velocity.
So…What is the difference between speed
and velocity?
• SPEED- reports the magnitude of distance
over time (just the number).
• VELOCITY- reports the magnitude AND
direction of motion.
So how do you calculate speed vs
velocity?
• Speed = distance / time
• Velocity = displacement / time
(Includes a direction!)
Are speed and velocity always going to
be the same?
• NO!
• Only if the object is moving in the SAME
direction the whole time.
• What is an example of a motion where avg
speed is not equal to average velocity? (demo)
Let’s look closer…
• Average velocity is calculated by the equation:
Vavg= (xf-xi) / (tf-ti)
Use the diagram to determine the average speed and average
velocity between the following points.
A. Going from A and B
B. Going from A to B and ending at C
•
Answers:
• A. Between A and B, speed and velocity will be
the same because they are in the same direction
the whole time.
– Speed = 180 m/min
– Velocity = 180 m/min east
• B. When the motion continues to point C, the
speed and velocity are different because the
distance traveled and displacement are different.
– Speed= 320 m/2 min= 160 m/min
– Velocity= 40 m/2 min= 20 m/min east
What is the coach's resulting
displacement and distance of travel?
Let’s use our math skills
• Page 323…
• Read through “MATH SKILLS”
• DO problems 1-3 “Practice Problems”
Answers to problems on 323
• 1. v=d/t
110m/72 sec= 1.5 m/s toward shore
2. v=d/t
38m/1.7 sec= 22m/s toward first base
3. d=vt=(12.0 km/hr)(5.00 hr)
=60.0 or 6.00 x 104 m southwest
Acceleration
Chapter 10.2-3
Try to define the
word
“acceleration”…
• Actual definition
is…any change in
VELOCITY
More specifically:
Acceleration is a change in velocity in a
period of time.
• So…Is it a vector or a scalar quantity?
– VECTOR
– It must include a direction (like velocity)
• This also means that you can change
acceleration by changing what?
– Speed or Direction
Does travel at a constant speed mean
you are not accelerating?
• NO!!!
• Remember that you can change velocity by
changing direction, thus CHANGING
ACCELERATION!
When a ferris wheel goes up and
around, what about its passengers is
changing?
1.
2.
3.
4.
Speed
Velocity
Acceleration
None of the above
So let me get this straight…
• Constant Speed means –
– Something travels the same distance in each time interval
• Constant Velocity means– Something travels the same distance, in the same direction in each
time interval
• So what about constant acceleration?
Constant Acceleration
• The velocity changes by the
same amt over each time
interval. (figure 11, p 329)
• Ex- centripetal acceleration
– As the earth goes around the
sun, it travels at a constant
speed
– BUT since it is going in a circle,
it’s velocity is changing AT A
CONSTANT RATE…therefore…
– CONSTANT ACCELERATION!
Causes of acceleration
• Increasing velocity
– Example: Car speeds up at green light
• Decreasing velocity
– Example: Car slows down at stop light
screeeeech
• Changing Direction
– Example: Car takes turn (can be at constant
speed)
Question
• How can a car be accelerating if its speed is a
constant 65 km/h?
• If it is changing directions it is accelerating
What do the numbers mean?
• Small acceleration – means speed is increasing
slowly
• Large acceleration- means speed is increasing
rapidly
Extension:
• Acceleration can be positive or negative, but
negative acceleration doesn’t always mean the
object is slowing down.
– (it could also be changing direction)
Calculating Acceleration
If an object is moving in a straight line…
• ∆V= change in velocity
 (Final Velocity – Initial Velocity) (m/s)
• A= acceleration
• ∆ T= time (s)
 (final time- initial time)

∆V
A ∆T
So what are the units of acceleration?


If A= V/T…
Acceleration is in m/s2
Calculating Acceleration
Acceleration = (Vf-Vi)
t
Let’s look at the picture below…what is
this car’s avg acceleration?
(16m / s  0m / s)
2

 4m / s
4s
0s
0 m/s
1s
4 m/s
2s
8 m/s
3s
12 m/s
4s
16 m/s
Question
• A skydiver accelerates from 20 m/s to 40 m/s in 2
seconds. What is the skydiver’s average
acceleration?
( Final _ velocity  Initial _ velocity )
A
Time
40m / s  20m / s 20m / s
2


 ( )10m / s
2s
2s
????
Constant velocity
Now consider a car moving with a rightward (+), changing velocity - that is, a
car that is moving rightward but speeding up or accelerating.
Acceleration
Distance time graphs
• Draw 2 graphs
– One showing a slow constant speed
– One showing a faster constant speed
Position-Time Graphs
Slow, Rightward(+)
Constant Velocity
Fast, Rightward(+)
Constant Velocity
More Position-Time Graphs
Slow, Leftward(-)
Constant Velocity
Fast, Leftward(-)
Constant Velocity
Consider a car moving with a constant, rightward (+) velocity - say of +10
m/s. A car moving with a constant velocity is a car with zero acceleration.
• Draw a graph!
Constant velocity = zero acceleration
Positive Acceleration
Now consider a car moving with a rightward (+),
changing velocity - that is, a car that is moving rightward
but speeding up or accelerating. Since the car is moving in
the positive direction and speeding up, the car is said to
have a positive acceleration.
Positive acceleration
Describe this graph!
• Does the velocity of the wind affect such
things as a sprinter’s speed or an airplane’s
flight time?
Resultant Velocity animation
• http://www.glenbrook.k12.il.us/GBSSCI/PHYS/
mmedia/vectors/plane.html
“Adding Vectors” Example:
A small airplane heads east with a speed of
200 mph with respect to the air (the “air speed”).
This would be the plane’s speed if
the air was NOT moving – no wind)
• If the wind/jet stream is moving east at 50 mph,
what is the plane’s resulting velocity with respect
to the ground (the “ground speed”)?
200
50
250 mph, east
with the wind
• If, later, the airplane is flying west into
the 50 mph wind with an “air speed” of
200 mph, now what is the plane’s
resulting velocity with respect to the
ground (the “ground speed”)?
200
50 150 mph, west
against the wind
1. Find the velocity in m/s of a swimmer who
swims 110 m toward the shore in 72 s.
• 1.5 m/s toward the shore
1. Imagine that you could ride a baseball that is
hit high enough and far enough for a home
run. Using the baseball as a reference
frame, what does the Earth appear to do?
1. Calculate the displacement in meters a
cyclist would travel in 5.00 h at an average
velocity of 12.0 km/h to the southwest.
But first let’s look at some graphs…
Distance
• If I wanted to graph speed, what should I label my
axes???
Time
• So the slope of the line=SPEED
Constant Speed
• What would a position-time graph look like for
a constant speed?