Physics of Motion
Physics of Motion
Frame of Reference- background or
object that shows a change in
position.
Ex. Earth or the Horizon
Fixed in place. If an object is moved
from here we have had some kind of
motion.
What is the difference
between speed and
acceleration?
Can a car be speeding
very fast and have zero
acceleration?
Speed
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Speed is a measure of how much
distance is covered in a given
amount of time.
It’s one example of a rate.
Speed is a distance divided by a time
S = D/ T
UNITS
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Any distance unit
and any time unit
can be used to
define a speed
Examples km/hr,
meters/sec, mi/hr,
cm/sec, light
years/century etc.
Comparing Units
20 km/h
12 mi/h
6 m/s
40 km/h
25 mi/h
11 m/s
60 km/h
37 mi/h
17 m/s
80 km/h
50 mi/h
22 m/s
100 km/h
62 mi/h
28 m/s
120 km/h
75 mi/h
33 m/s
200 km/h
?
?
Comparing Units
20 km/h
12 mi/h
6 m/s
40 km/h
25 mi/h
11 m/s
60 km/h
37 mi/h
17 m/s
80 km/h
50 mi/h
22 m/s
100 km/h
62 mi/h
28 m/s
120 km/h
75 mi/h
33 m/s
200 km/h
120 mi/h
?
Comparing Units
20 km/h
12 mi/h
6 m/s
40 km/h
25 mi/h
11 m/s
60 km/h
37 mi/h
17 m/s
80 km/h
50 mi/h
22 m/s
100 km/h
62 mi/h
28 m/s
120 km/h
75 mi/h
33 m/s
200 km/h
120 mi/h
60 m/s
Check for Understanding
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On your team’s whiteboard, write an
equation and solve for the average
speed when Betty swims 50.0
meters in 27.4 seconds. Be sure to
use correct units and state your
answer in two or three significant
figures.
S = D/T = 50.0m/27.4 s = 1.82 m/s
Car Trip
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D = 1.22 m
T = 1.13 s
1.37 s
Use T = 1.25s
S = D/T = 1.22m / 1.25 s = 0.976
m/s = 0.98 m/s = 1.0 m/s
Instantaneous vs. Average Speed
vs. Constant Speed
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Instantaneous speed is speed at a
particular instant
Constant speed never changes
Average speed is total distance
covered for a trip divided by total
time elapsed
average speed = total
distance/time
Check for Understanding

What is the difference between
instantaneous and average speed?
Examples

Find the average speed of a car trip
covering 480 km in 6.0 hrs (be sure
to write the symbolic equation first)
S = distance/time = D/T =
480 km/ 6.0 h = 80. km/h (note
that it’s two significant figures)
What’s Unknown?
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Start with S = D/T and find an
equation for
D = SxT
and an Equation for T = D/S
Memory Trick
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D=SxT
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S = D/T

T = D/S
When solving problems, always
write the symbolic equation first
D
S
T
Remember your Algebra
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S = D/T ; multiply both sides by T
SxT=D
D = S x T; divide both sides by S
D/S = T
T = D/S
When solving problems, always write the symbolic equation first.
Then an equal sign, then put in the known numbers, then solve.
Distance Unknown
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Find the distance covered by a horse
running 18 m/s for one minute
D = S x T=18 m/s x 60 sec =1080 m
Try another one; How far can Sarah run if
she averages 4.5 m/s for three minutes
and 20 seconds? (What are we going to
write first?)
D = S x T = 4.5 m/s x 3.0 min x 60s/
1minute = 810 m
Question
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How long does it take a snail
creeping at 1.0 cm per second to
cross a 2.0 meter walkway?
T = D/S
T = 200 cm/ 1.0 cm/s
T = 200 s
T = 3 minutes 20 seconds
Word Problem Practice
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Write a symbolic equation for this
sentence:
How long does it take for the
Metroliner train to go from NY to
Boston, which are 520 km apart, if it
averages 127 km/hr?
Now write in the numbers
Now find the answer
Check for understanding

Does a speedometer measure
average speed or instantaneous
speed?
Courtesy of CobraCountry.com
Unit Conversion
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Suppose we want to convert 25 m/s
to km/hour
25 m/s x 1 km/1000m x 3600s/1
hour = 90 km/hr
This is called the factor-label method
You Try It
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Convert 125.0 km/hr to meters/sec
125.0 km/hr x 1000m/1 km x 1
hr/3600 sec = 34.7 m/s
Another word for the “labels” in this
method would be the ???
Velocity
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Velocity is speed in a
given direction
Constant velocity
requires both constant
speed and constant
direction
Is a car traveling on a
circular track at
steady speed moving
at constant velocity?
NO! It’s direction is
continually changing.
Acceleration
Acceleration
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How fast velocity changes
Acceleration = change of
velocity/time
Includes increases and decreases of
speed and changes in direction
Acceleration (+) Deceleration (-)
a= Vf- Vi/ t
Acceleration = a Time = t
Vf = Final Velocity Vi= Initial Velocity
Acceleration Equations
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a= Vf-Vi/t
t = Vf-Vi/a
Vf = (a x t) + Vi
Vi = Vf – (a x t)
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UNITS MUST MATCH!
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Finding Acceleration
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A car steadily increases its speed
each second from 35 to 40 to 45
km/h. What is its acceleration?
Answer: 5 km/h/s
In 10 seconds a train increases
speed from 20 km/h to 40 km/h.
What is its acceleration?
a = 20km/h ÷ 10s = 2.0 km/h/s
Free Fall
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Time to
fall(s)
In free fall an
object’s speed
increases by about 0
10 m/s in each
1
second.
v = gt = 9.8t
2
g = 9.8 m/s/s
g = 9.8 m/s2
Speed
(m/s)
0
9.8
19.6
3
29.4
4
39.2
5
49
More on Free Fall
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Due to gravity a = 9.8 m/s2= g
v = gt
Instantaneous speed = acceleration
x time
Question: What is the speed of a
rock that has fallen from rest for 5.5
seconds? (without air resistance)
Galileo’s Experiment

Which would reach
the ground first, a
marble or a
cannonball?
Courtesy Dan Heller Photography
Rising and Falling Rock
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A rock is thrown upward with 20
m/s. It rises then falls to the height
from which thrown. What will be its
speed at that height? It’s velocity?
Answer 20 m/s
(down)
Gravity takes speed away on the way up at 9.8 m/s/s and then
gives it back on the way down, at the same rate
Distance Fallen
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What is average speed of an object that
falls for 1 second? 5 m/s, average of 0 and 10
What is distance fallen in this time?
5m = 5 m/s x 1s
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What is average speed during second
second of fall?
15 m/s, average of 10 and 20
What is distance fallen in second second?
15m = 15m/s x 1s
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What is distance fallen in first two
seconds?
20m = 5m + 15m
The Pattern
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Distance fallen in t
seconds
d = 1/2gt2
Now if the object is in
motion, then you have
to account for that as
well.
d= vit +
1/2gt2
time
distance
1
5
2
20
3
45
4
80
5
125
Falling Apple
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An apple drops from the tree and
hits the ground in two seconds
What is its speed when it hits?
What is its average speed?
How high did it fall from?
Free Fall Problem
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A person is standing on top of a roof,
holding two objects. The person
drops item A and at the same time
throws item b straight up over the
edge of the building with an initial
speed of 25 m/s. If the building
itself is 450 m high, how long will it
take both objects to hit the ground
and at what speed will they hit the
ground with?
Helicopter Problems
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1. A Helicopter is rising 5.0 m/s and
someone drops a bag from it. After
two seconds, what is the bags
velocity, how far has the bag fallen
and how far below the helicopter is
the bag?
2. The helicopter in problem one
now descends 5.0 m/s. After two
seconds, what is the bags velocity,
how far has the bag fallen and how
far below the helicopter is the bag?
Weather Balloon Problem
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A weather balloon is floating upward
at 2.5 m/s above the Earth when it
releases a pack of instruments.
A. If the pack hits the ground with a
velocity of 73.5 m/s how far did the
pack fall?
B. How long did it take for the pack
to fall?
Air Resistance
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Why, on earth,
does a coin reach
the ground faster
than a feather?
What would
happen on the
moon?
Confused?
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Explain the difference between velocity
and acceleration and velocity?
Is acceleration an example of a velocity?
Can an object with zero velocity be
accelerating?
At the top of its path, the velocity of a
rock thrown upward is ________?
At the top, its acceleration is _______?