GOAL
To describe motion using vocabulary, equations, and
graphs.
HOW WOULD YOU DESCRIBE AN A OBJECT’S MOTION?
The answer depends on your perspective -- your frame of reference
Example: Even while sitting in the classroom appearing
motionless, you are moving very fast.
• Rotating 0.4 km/s (0.25 mi/s) around the center of the
Earth
• Revolving 30 km/s relative to the Sun
• Revolving 250 km/s with the solar system around the
center of the milky way galaxy
• Moving 600 km/s with the Milky Way away from the center
of the universe, towards the constellation Hydra
The Sea
Serpent
When we discuss the motion of something, we describe its motion
relative to something else.
A frame of reference is a perspective from which a
system is observed together with a coordinate system
used to describe motion of that system.
Example:
You drive your car home from school at speed of 30 mph.
… your frame of reference is relative to road
…. Your coordinate system has a starting point (origin) at school and
a positive direction towards home
We also discuss motion using simplified models, such as the
particle model.
The movement of an object through space can be quite complex.
There can be internal motions, rotations, vibrations, etc…
Example:
This motion is complex!
But, if we ignore the shape of the hammer and
treat it as a particle moving through space, we can
greatly simplify the motion – making it much
easier to make predictions
Displacement
Displacement is the change in position of an object
Δ x = xf – x i
(Change in postion = final position – initial position)
P
Q
path;
length is distance traveled
Displacement is a vector quantity, so it tells
us how far an object is from its starting
position and in what direction
Note: Traditionally, the coordinate
system for displacement is positive for
displacement upwards or towards the
right, and negative for displacement
downwards or towards the left.
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_
_
Sometimes, it might be convenient to
change that system, but if so, YOU MUST
DEFINE THE COORDINATE SYSTEM IN
THE PROBLEM
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VELOCITY
• Change in the position of an object over time.
Without velocity, there is no change in position!
𝑣𝑎𝑣𝑔 =
∆𝑥
∆t
=
𝑥𝑓 −𝑥𝑖
𝑡𝑓 −𝑡𝑖
Average velocity = change in position / change in time
• Velocity is a vector quantity. It goes in the same direction
as the change of position.
+
_
+
_
VELOCITY EXAMPLE PROBLEMS
1. If Joe rides south on his bicycle in a straight line for 15
minutes with an average speed of 12.5 km/hr, how far
has he ridden?
2. Simpson drives his car with an average velocity of
48.0km/h to the east.
a) How long will it take him to drive 144 km?
b) How much time will he save by increasing his average
velocity to 56.0 km/h to the east?
VELOCITY EXAMPLE PROBLEMS
1. If Joe rides south on his bicycle in a straight line for 15
minutes with an average speed of 12.5 km/hr, how far
has he ridden?
𝑣𝑎𝑣𝑔 =
∆𝑥
∆t
 𝑣𝑎𝑣𝑔 ∗ ∆t =∆𝑥
12.5 km/hr * (15 minutes * 1 hr/ 60 minutes) = ∆𝑥
∆𝑥 = 3.13 km South
VELOCITY EXAMPLE PROBLEMS
2. Simpson drives his car with an average velocity of
48.0km/h to the east.
a) How long will it take him to drive 144 km?
b) How much time will he save by increasing his average
velocity to 56.0 km/h to the east?
∆𝑥
𝑣𝑎𝑣𝑔 = ∆t  ∆𝑥 / 𝑣𝑎𝑣𝑔 = ∆t
144 km / (48.0 km/hr) = 3.00 hours
144 km / 56.0 km/hr = 2.57 hours.
3.00 hours – 2.57 hours = 0.43 hours or 25.8 minutes
VELOCITY PROBLEMS FOR INDIVIDUAL
PRACTICE
1. It takes you 9.5 minutes to walk with an average velocity
of 1.2 m/s to the north from the bus stop to the museum
entrance. What is your displacement?
2. A bus travels 280 km south along a straight path with an
average velocity of 88 km/h to the south. The bus stops
for 24 minutes, then it travels 210 km south with an
average velocity of 75 km/h to the south.
a) How long does the total trip last?
b) What is the average velocity for the total trip?
VELOCITY PROBLEMS FOR INDIVIDUAL
PRACTICE
1. It takes you 9.5 minutes to walk with an average velocity
of 1.2 m/s to the north from the bus stop to the museum
entrance. What is your displacement? 680 m North
2. A bus travels 280 km south along a straight path with an
average velocity of 88 km/h to the south. The bus stops
for 24 minutes, then it travels 210 km south with an
average velocity of 75 km/h to the south.
a) How long does the total trip last? 6.4 hours
b) What is the average velocity for the total trip?
76 km/hr South
VELOCITY TERMINOLOGY
So far we’ve talked about average velocity, defined as change in
position over change in time.
∆𝑥
𝑣𝑎𝑣𝑔 =
∆t
Sometimes, of course, our velocity fluctuates from moment to
moment.
Instantaneous velocity is the speed and direction of motion at a
particular instant in time.
Uniform motion describes any motion where the velocity does NOT
fluctuate, but instead remains constant. The only equation we
need to describe uniform motion is the one above.
Real – world example:
Your car’s speedometer tells you
instantaneous speed. If your car also has a
compass, then you know your
instantaneous velocity!
POSITION VS TIME GRAPHS
Motion is often represented graphically. One such graph
is a position – time graph, where position is on the yaxis and time is on the x axis.
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Position
(m)
Coordinate system
Describe the bike’s motion.
The bike is moving to the right
at constant velocity.
Time (hr)
HOW CAN I TELL?
• A straight line on a position vs time graph = constant velocity
• A positive slope (as time increase, position increases) means
that the bike is moving an a positive direction (right).
+
POSITION VS TIME GRAPHS
Motion is often represented graphically. One such graph
is a position – time graph, where position is on the yaxis and time is on the x axis.
_
Position
(m)
Describe the bike’s motion.
Time (hr)
The bike is moving to the left
at constant velocity.
HOW CAN I TELL?
• A straight line on a position vs time graph = constant velocity
• A negative slope (as time increases, position decreases)
means that the bike is moving an a negative direction (left).
+
POSITION VS TIME GRAPHS
Motion is often represented graphically. One such graph
is a position – time graph, where position is on the yaxis and time is on the x axis
_
Position
(m)
Describe the bike’s motion.
The bike isn’t moving!
Time (hr)
HOW CAN I TELL?
• The position is the SAME at every time interval – no change in
position, no movement.
• The slope is zero = no movement
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POSITION VS TIME GRAPHS (WE DO)
1. A bus drives 40 km/hr to the east for 20 minutes,
then stops for 5 minutes, then drives 50 km/hr to the
west for 10 minutes. Draw the motion graph.
POSITION VS TIME GRAPHS (WE DO)
Position to the East
1. A bus drives 40 km/hr to the east for 20 minutes,
then stops for 5 minutes, then drives 50 km/hr to the
west for 10 minutes. Draw the motion graph.
13.3
km
5 km
5
10
15
20
25
30
35
Time (minutes)
POSITION VS TIME GRAPHS (WE DO)
Position to the North
2. Describe the motion of the ladybug shown in the
graph below.
4m
3m
2m
1m
5
10
15
20
25
30
35
Time (seconds)
POSITION VS TIME GRAPHS (WE DO)
Position to the North
2. Describe the motion of the ladybug shown in the
• The lady bug is stationary at position 4 m N for 10
graph below.
seconds,
• then it moves 0.6 m/s South for 5 seconds,
• then it moves 0.1 m/s North for 10 seconds,
• Then it is stationary at position 2 m N for 10
seconds
4m
3m
2m
1m
5
10
15
20
25
30
35
Time (seconds)
POSITION VS TIME GRAPHS (WE DO)
3. Graph the data on a position – time graph and
compare the average velocity of each car.
Car A
Car B
Time (min) Position (km)
Time (min
Position (km)
0
8
0
10
10
18
10
20
20
28
20
30
30
40
30
40
40
54
40
50
POSITION VS TIME GRAPHS (WE DO)
3. Graph the data on a position – time graph and
compare the average velocity of each car.
60
Average velocity of Car A:
1.4 km/min
50
Position (km)
40
30
Car A
20
Car B
10
Average velocity of Car B:
1.3 km/min
Are either of the cars traveling
at constant velocity?
0
0
10
20
Time (minutes)
30
40
Are either of the cars
accelerating?
POSITION VS TIME GRAPHS (WE DO)
3. Graph the data on a position – time graph and
compare the average velocity of each car.
60
Average velocity of Car A:
1.4 km/min
50
Position (km)
40
30
Car A
20
Car B
10
Average velocity of Car B:
1.3 km/min
Are either of the cars traveling
at constant velocity? Car B
0
0
10
20
Time (minutes)
30
40
Are either of the cars
accelerating? Car A
POSITION VS TIME GRAPHS (YOU DO)
Position (km) East
1. A car drives 50km/hr North for 30 minutes, then
stops for 15 minutes, then drives 40 km/hr South for
1 hour. Draw a position – time graph.
2. Describe the motion of the bicyclist in the positiontime graph below.
20
15
10
5
10
20
30
Time (minutes)
40
50
POSITION VS TIME GRAPHS (YOU DO)
3. Plot the motion of the bus on a graph and calculate
the bus’s average velocity.
Time (minutes)
Position (km South)
0
30
5
30
10
10
15
-10
20
-10
35
5