Linear Motion
Linear Motion
All Motion is Relative
• This means when we describe motion
we do it relative to something
• The Train is leaving the station or is
the station leaving the train?
Linear Motion
All Motion is Relative
• Even as we stand still
– Rotating (30o N) @ 1500 kilometers/h
– Revolving around sun @107,000 km/h
– Galaxy milling around @ 70,000 km/h
– Galaxy revolving @ 792,000 km/h
– Galaxy outward @ 2.1 million km/h
Linear Motion
• A car in the Indy 500 ends up at the
same point.
• On the school bus traveling at 30mph
you throw a ball to a classmate, how
fast is the ball moving?
• We usually describe motion relative
to the surface of the earth
Linear Speed
• Speed is a “scalar quantity”
– does not include direction.
• I am running at 10 mph, but I do
not tell you where – this is speed.
• Speed is my distance covered
divided by the time it takes me
Linear Speed
•
•
•
•
mi/h (mph) – Miles per hour
km/h – Kilometers per hour
m/s – Meters per second
Light-years / century
• The symbol / is read as “per”
Speed is a ____ quantity.
A.) vector
B.) scalar
C.) additive
D.) subtractive
A child walks 5.0 meters north,
then 4.0 meters east, and finally
2.0 meters south. What is the
magnitude of the resultant
displacement of the child after the
entire walk?
(A) 1.0 m
(B) 5.0 m
(C) 3.0 m
(D) 11.0 m
If I travel for 2 hours at 20
miles per hour the total
distance covered is ?
Linear Speed
Speed
• Measure of how fast something moves
• Unit of distance divided by unit of time
• Two types of measurement
– Instantaneous speed
– Average Speed
Linear Speed
Instantaneous Speed
• You are in a car heading downtown, as
you can see from the speedometer your
speed is 40 mi/h.
• Downtown is 10 miles away at this
speed, how long will it take you?
• IS THIS TRUE???
Linear Speed
Average Speed
• It would take us a lot longer than 15
minutes to drive downtown because of
the traffic where we have to slow, stop,
start, accelerate, slow, stop, etc., etc,.
Linear Speed
Average Speed
• Therefore in planning a trip we think
about average speed
• Average Velocity
– Total distance (d) covered/ time (t)
v = d2 – d1
t
• If Downtown is 10 miles and
it will take me 30 minutes when
my average speed is 20 mi/h
• This is a lot different from an instantaneous
speed of 40 mi/h.
• If we know our average speed and the time
traveled we can arrange the formula to tell us
our distance traveled.
• Total distance = Avg speed x time
d = vt
Linear Velocity
• Velocity is a “vector quantity”
– this means is has Speed and Direction
• If a car travels at of 60 km/h we
have defined its speed
• If we say it is traveling at 60km/h
heading north we have defined its
Velocity!
• Going in a straight line at the same
speed is called Constant Velocity.
• But if we change our speed (brake at
a light) or our direction (turn a
corner) then we have a Changing
Velocity
• Changing our speed or direction is
Acceleration
Velocity has
A) speed
B) direction
C) force
D) A and B
On a highway, a car is driven 80
kilometers during the first 1.00 hour
of travel, 50 kilometers during the
next 0.50 hour, and 40 kilometers in
the final 0.50 hour. What is the car’s
average speed for the entire trip?
(A) 45 km/h
(B) 60. km/h
(C) 85 km/h
(D) 170 km/h
Linear Acceleration
• Acceleration is how quickly velocity
changes
a = v2 – v1
t
• When we accelerate in a car from
stop to 60km/h in 5 seconds.
a = (60 km/h – 0 km/h)/5s
= 12 km/h/s
Linear Acceleration
• We have changed our speed and this is
Acceleration.
• The same applies when we are in a car that
slows – this is called negative acceleration
or Deceleration
• When we brake to a stop from 60km/h in 5
seconds.
a = (0 km/h – 60 km/h)/5s
= – 12 km/h/s
• Acceleration also applies to changes
in direction.
• We feel the effects when in a car we
are pushed to the side when we turn
a sharp corner
• Acceleration is measured in km/hr/s,
but usually m/s2 in Physics
A skater increases her speed uniformly
from 2.0 m/s to 7.0 m/s in 12 seconds.
What is her acceleration?
For the next 20 seconds she continues at
the same speed. What is her
acceleration?
She next applies her brakes and stops in
2 seconds. What is her acceleration?
A motocross rider accelerates from
rest at 9 m/s2 for 4.3 seconds. What
is his final speed?
As he approaches a curve he
accelerates at -1.5 m/s2 for 2.2
seconds. What is his new speed?
Free Fall – How Fast
• If a rock is dropped off the side
of a cliff we would expect it to
fall and during the fall we would
expect it to accelerate.
• If there was no air resistance its
speed would increase by approximately
10m/s every second.
In m/s2, what would be its acceleration?
Free Fall – How Fast
• After 5 seconds
– What would be its speed?
– v = at
– v = 10 m/s2 (5 s) = 50 m/s
• Acceleration due to gravity is referred to
as g and is accurately 9.8 m/s2
Time
0
Velocity
final
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125
Free Fall
• If the rock was thrown up into the air we
would still see the rate of velocity change
as -10m/s2.
• But for the first few seconds it would be
decelerating, then stopped for a fraction
of a second, before it started its
acceleration toward the ground at 10m/s2.
V initial = 30 m/s up
Time
0
Velocity
final
30
VAvg
Y this
second
Total Y
30
0
0
V initial = 30 m/s up
Time
VAvg
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Velocity
final
30
1
20
25
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second
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0
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25
V initial = 30 m/s up
Time
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Velocity
final
30
Y this
second
Total Y
0
0
1
20
25
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40
V initial = 30 m/s up
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final
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Y this
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Total Y
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0
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V initial = 30 m/s up
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0
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-5
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V initial = 30 m/s up
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final
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second
Total Y
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0
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V initial = 30 m/s up
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Velocity
final
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Total Y
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0
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-30
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0
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-30
-25
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-40
-35
-35
-35
Acceleration due to gravity is
approximately what value?
A) 12 m/s2
B) 9.8 m/s2
C) 7 m/s2
D) 0 m/s2
A ball thrown vertically upward
reaches a maximum height of 30
meters above the surface of Earth.
At its maximum height, the
acceleration of the ball is
(A) 0.0 m/s2
(B) 3 m/s2
(C) 9.8 m/s2
(D) 24 m/s2
A ball thrown vertically upward
reaches a maximum height of 30
meters above the surface of Earth.
At its maximum height, the speed
of the ball is
(A) 0.0 m/s
(B) 3 m/s
(C) 9.8 m/s
(D) 24 m/s
A ball thrown vertically upward
reaches a maximum height of 30
meters above the surface of Earth.
The amount of time to teach its
maximum height is
(A) 0.0 s
(B) 3 s
(C) 9.8 s
(D) 2.4 s
Apollo 15
commander
David R. Scott
confirmed
Galileo's
hypothesis that
in the absence
of air resistance
all objects fall
with the same
velocity.
Free Fall – How Far?
• But there is air resistance on earth.
• So???
• Would you rather jump out of a plane
with or without a parachute?
• Why?
Free Fall – How Far?
• At the end of the first second of something
falling is has a instantaneous speed of 10m/s.
• But this does not mean it has fallen 10m in
the first second
• This is where the difference between average
speed and instantaneous speed comes in
• It started at zero, so we know the average
speed is somewhere between 0 and 10m/s
Free Fall – How Far?
• The distance traveled by an object
starting at rest and uniformly
accelerating is:
d= ½ gt2
Time
0
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final
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V initial = 30 m/s up
Time
0
Velocity
final
30
VAvg
Y this
second
Total Y
30
0
0
V initial = 30 m/s up
Time
VAvg
0
Velocity
final
30
1
20
25
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second
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0
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V initial = 30 m/s up
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Velocity
final
30
Y this
second
Total Y
0
0
1
20
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25
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40
V initial = 30 m/s up
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final
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Y this
second
Total Y
0
0
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20
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V initial = 30 m/s up
Time
VAvg
0
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final
30
Y this
second
Total Y
0
0
1
20
25
25
25
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15
15
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0
5
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-5
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V initial = 30 m/s up
Time
VAvg
0
Velocity
final
30
Y this
second
Total Y
0
0
1
20
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25
25
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15
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3
0
5
5
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-10
-5
-5
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-15
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V initial = 30 m/s up
Time
VAvg
0
Velocity
final
30
Y this
second
Total Y
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0
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5
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-5
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5
-20
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-15
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-30
-25
-25
0
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VAvg
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Velocity
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30
Y this
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Total Y
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0
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-5
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-15
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6
-30
-25
-25
0
7
-40
-35
-35
-35
A sky diver free falls for
twelve (12) seconds. What is
her final velocity in m/s?
2
Use g = 10 m/s
Ignore air resistance
A sky diver free falls for
twelve (12) seconds. What is
is the distance that she falls?
2
Use g = 10 m/s
Ignore air resistance
Several years ago a car load of
teenagers were coming down the
Crest Highway too fast. They
went off a cliff and fell 320-m
(1050 feet). How long were they
in the air before they crashed?
2
Use g = 10 m/s
Ignore air resistance
Air Resistance
• As we said before in a
vacuum a stone and a
feather will fall at the
same rate.
• But we know here on
Earth that does not
happen
• If you were jumping
out of a plane, what
shape would you like
your parachute to be?
Why?