CHAPTER 1
MOTION & MOMENTUM
SECTION 1
WHAT IS MOTION?
• All matter is constantly in MOTION
• Motion involves a CHANGE in position.
– An object changes position relative to a
REFERENCE POINT.
– DISTANCE is the total length of the route
an object travels when it moves.
– DISPLACEMENT includes direction of the
stopping point from the starting point.
DISTANCE
D=10 meters
A
B
Reference point
When going from point A to point B
motion occurred because you traveled
A distance (10 meters) from your
Reference point (A).
DISPLACEMENT
B
N
W
E
D = 50 M
S
D = 30 M
A
D = 40 M
DISTANCE = 70 METERS (40M + 30M = 70M)
DISPLACEMENT = 50 M northeast
QUESTION:
IS IT POSSIBLE TO HAVE A DISTANCE OF 140 M
BUT HAVE A DISPLACEMENT HAVING 0 M?
EXPLAIN YOUR ANSWER.
ATTENTION!!!
• SPEED & VELOCITY ARE ALMOST
THE SAME THING
• BOTH TELL YOU HOW FAST YOU
ARE GOING
• ONLY DIFFERENCE……
• SPEED MEANS HOW FAST
• VELOCITY MEANS HOW FAST + A
DIRECTION
Velocity is the distance traveled divided by the
time taken to travel the distance + a direction
Formula:
VELOCITY = DISTANCE
TIME
Mrs. M walked 10 m across
the room (that way) in 5 s.
Mrs. M traveled at a speed of
2 m/s.
or
V= d
t
10 m
v= 5s
m
v=2 s
That way
That way
• The units of velocity are units of
distance divided by units of time
– V = velocity
– d = distance
– t = time
• The SI (system international) unit for
velocity is meters per second (m/s)
or
m
s
RULE
• IF VELOCITY DOESN’T GIVE YOU A
DIRECTION YOU DON’T HAVE TO
INCLUDE ONE….
• IF IT DOES THEN YOU MUST
INCLUDE IT.
• SIMPLE….
• An object in motion can change
VELOCITY many times as it moves
from one point to another:
– Speeding up
– Slowing down
– CHANGING DIRECTION
• AVERAGE VELOCITY is the total distance
traveled divided by the total time taken.
• INSTANTANEOUS VELOCITY is the object’s
speed at a particular moment in time.
• CONSTANT VELOCITY occurs when an
object travels at a steady rate with the same
instantaneous speed for some period of time
EXAMPLES
• JOE DROVE 100 MILES IN 2 HOURS
– HIS VELOCITY WAS 50 MILES PER HOUR
• MARY DROVE 100 MILES IN 2 HOURS
– HER VELOCITY WAS ALSO 50 MILES PER
HOUR
AVERAGE VELOCITY
• ALONG THE WAY JOE HIT TRAFFIC,
HE CONTINUALLY WAS SPEEDING
UP AND SLOWING DOWN. HE STILL
MADE IT TO HIS DESTINATION IN 2
HOURS HIS AVERAGE VELOCITY
WAS 50 MILES / HOUR.
INSTANTANEOUS
VELOCITY
• WHILE JOE WAS DRIVING HE GOT STUCK
BEHIND A TRAFFIC JAM. IN ORDER TO
MAKE UP SOME TIME HE HIT THE GAS
AND BLEW RIGHT PAST THE STATE
POLICEMAN AND WAS PULLED OVER.
“SIR, STATED THE POLICEMAN, DO YOU
KNOW HOW FAST YOU WERE GOING? I
HAD YOU CLOCKED AT 85 MILES / HOUR.
AND THAT CLASS IS AN EXAMPLE OFINSTANTANEOUS
VELOCITY. THE MOMENT JOE PASSEDTHE COP
HE WAS TRAVELING 85 MILES / HOUR.
CONSTANT VELOCITY
• MARY BEGAN HER JOURNEY.
THERE WAS NO TRAFFIC THAT DAY.
AS SOON AS SHE STARTED GOING
50 MILES / HOUR SHE POPPED ON
THE CRUISE CONTROL AND
TRAVELLED MARILY ON HER WAY.
• MOTION can be graphed on a
distance-time graph
– Time plotted on the horizontal axis (x - axis)
– Distance plotted on the vertical axis (y - axis)
5m
distance 4m
3m
2m
1m
1s
2s 3s 4s 5s
time
6s
• The steeper the line on a distance-time
graph, the GREATER the VELOCITY
Much faster
fast
5m
distance 4m
3m
2m
1m
1s
2s 3s 4s 5s
time
6s
• A horizontal line on a distance-time
graph indicates that no change in
position is occurring and the VELOCITY
is zero.
5m
distance 4m
3m
2m
1m
1s
2s 3s 4s 5s
time
6s
• Velocity is the speed of an object and
its direction of motion.
– Velocity changes if either, or both of these
change.
Speed vs. Velocity
• Speed is how fast an object is traveling
• Velocity is how fast an object is
traveling and also the direction!!!
Section 2
Acceleration
• Acceleration - change in velocity divided by
the time for the change to occur.
– Changes include:
• Speeding up
• Slowing down
• CHANGING DIRECTION
• Can be calculated if you know the object’s
velocity
changed during a given time
period.
Formula
ACCELERATION = (FINAL VELOCITY – INITIAL VELOCITY)
TIME
a=
(Vf - Vi)
t
• The unit for acceleration is:
– Distance divided by time squared
• The SI unit for acceleration is:
– Meters per second squared
m
s2
ADVANCED ONLY!!!
• PHYSICS BOOKS (WHEN YOU ARE
IN 11TH GRADE) refer to this as this
formula:
ΔV
____
a=
t
Δ – (greek letter delta) means “change in”
this is the equivalent to something –
something else.
Example 1
• If you had five apples and ate
three…the change would be 2 apples
left.
• Therefore Δ apples would be 2 apples.
Example 2
•
•
•
•
You were going 10 m/s
Then slowed down to 6 m/s
Your change in velocity was 4 m/s
ΔV = 4 m/s
In PhYsIcS
•
•
•
•
•
There is no speeding up…
No slowing down…
Just + (positive)
And – (negative)
Remember: you either positively
accelerate or negatively accelerate.
• NEVER Decelerate!!!!!! It does not exist
• Acceleration is POSITIVE when an
object SPEEDS UP.
• Acceleration is NEGATIVE when an
object SLOWS DOWN.
Example #1
A dog sat on the sidewalk. The dog saw
his master and ran at 4 meters per
second in 2 seconds. What was the
dog’s acceleration?
Vi = 0
m
s
Vf = 4
t=2s
a=
(Vf - Vi)
t
m
s
(4
a=
m
s
-0
2s
a=4
m
s
2s
a=2
m
s2
m
s
)
Example #2
• A dog was walking at a Velocity of 4
meters per second west. The dog came
to a stop in 2 seconds. What was the
dog’s acceleration?
Vi = 4
m
s
sf = 0
t=2s
m
s
west
west
a=
(vf - Vi)
t
(0
a=
m
s
west
2s
m
-4
a=
s
2s
a =-2 m west
s2
west
-4
m
s
west
)
Velocity - Time graph
• Graphing acceleration:
– Velocity on vertical axis (y - axis)
– Time on horizontal axis (x - axis)
• An object speeding up will have an
upward slope.
5
velocity (ms ) 4
3
2
1
1s
2s 3s 4s 5s
time
6s
• An object slowing down has a
downward slope.
5
velocity ( ms ) 4
3
2
1
1s
2s 3s 4s 5s
time
6s
• A horizontal line means NO acceleration
or (zero).
5
Velocity ( ms ) 4
3
2
1
1s
2s 3s 4s 5s
time
6s
momentum
Section 3
• Mass - the amount of matter in the object.
– The SI unit for mass is kg.
– Weight of an object is related to its mass.
– A bowling ball has more mass than a pillow and
weighs more.
– However the pillow is larger than a bowling ball.
– DO NOT LET SIZE OF AN OBJECT FOOL
YOU!!!
• Inertia - tendency of an object to resist a
change in its motion.
• The more mass an object has the harder it is
to speed it up, slow it down, or turn it.
• Momentum - a measure of how difficult
it is to stop a moving object.
– Equals the product of mass and velocity
• We know the faster a bicycle moves,
the harder it is to stop.
• If fact by increasing the velocity or
increasing its mass will make anything
harder to stop.
Momentum
• The symbol used to signify momentum
is the letter “p”
• The equation is written as:
p = mv
• p - momentum
• m - mass
• v - velocity
• The SI unit for momentum is:
kg . m/s
kilograms multiplied by meters per second
Momentum Equation
m = 14 kg
m
v = 2 s north
p=?
P = mv
m
P = (14 kg) x (2 s north)
P = 28 kg . ms north
• Law of conservation of motion - states that
the total momentum of objects that collide
with each other is the same before and after
the collision.
• When playing pool the cue ball moves
towards the other balls. When the cue ball
collides with the other balls the cue ball slows
down and it decreases its momentum.
However the other balls speed up and
change direction. The other balls are
increasing their momentum. The momentum
of the cue ball was transferred into the other
balls.
• So what slows down the other balls?
• Outside forces such as gravity and
friction are almost always acting on
objects during a collision.
• These forces are small and can be
ignored.
After Collisions
• Objects could
– stick together
– Collide and bounce off