Phy 521
What is physics
Physics is the branch of knowledge that studies the physical world.
Physicists investigate objects as small atoms and as large as
galaxies. They study the nature of matter and energy and how they
are related. Physics is the study of motion and energy. Physicists
and other scientists are inquisitive people who look at the world
around them with questioning eyes. Their observations lead them
to search for the causes of what they see. What makes the sun
shine? How do the planets move? Of what is matter made? More
often than not, finding explanations to the original questions lead
to more questions and experiments. What all scientists hope for
our powerful explanations that describes more than one
phenomenon and lead to a better understanding of the universe.
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or
Physics is
PHUN
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Kinematics
Where do you see motion in your life?
•Birds flying
•Babies crawling
•Cars moving
•Sports
Anytime something is in motion it involves kinematics.
Kinematics: is the study of “how” objects move.
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Section 2 – 1: Picturing Motion
Frame of reference: situation where all measurements are
taken from a specific point of observation.
At rest: when the velocity of an object is the same as the
velocity of the reference frame which the object is in.
For example: moving screen behind people in a car being filmed.
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Following diagrams (page 32 of text) show the change in a
runners position at equal time intervals. What inferences
can be made about the runners velocity in each different
case?
A) At rest,
B) Moving with constant velocity
C) Accelerating
D) Decelerating
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Section 2 – 2: Displacement and Velocity
Scalar: a quantity that has only magnitude or size. There is
no direction.
For example: 100 kg, 5 m Or 6 ml.
Vector: a quantity having both magnitude and direction
For example: 7 km North
(magnitude of 7, direction is North)
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Position: a given point with respect to an origin.
Distance: the measurement between two objects or separation.
For example: the distance between me and you is 5 feet
Displacement: the change in position of an object. This
quantity can be either positive or negative.
Speed: the magnitude of motion and is always positive.
For example, 40 km/hr
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Velocity: is the vector quantity for motion, having both
magnitude and direction.
For example 40 km/hr East
(magnitude of 40, direction is East)
Velocity can be found using the following formula
d
vav 
t
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Acceleration: is the change in velocity with respect time. It is
a vector quantity having both magnitude and direction.
Clock reading: the specific time at that point.
Time interval: the difference in time between two successive
clock readings.
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Pg 39 of text
Do
#1,2 page 34 (pdf 9)
VDT WorkSheet # 1,2,3,4
# 1,2,3 page 45 (pdf 10)
# 1-6 Section Review (pdf 9)
Position Match Activity
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Section 2 – 3: Constant, Average, and Instantaneous velocity
Uniform Motion: moving at a constant velocity.
Non-uniform Motion: the velocity is changing either in
magnitude or and direction, or both.
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Graphs are an excellent tool for analyzing patterns of motion and
determining whether the motion is uniform or non-uniform.
Position time graphs can determine whether the motion is
uniform or non-uniform.
The slope of a position time graph represents the velocity.
If a graph consists of a straight line, the slope is constant
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A constant slope means, a constant velocity, therefor we have
uniform motion
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The slope of the line can be found using the following formula
rise y2  y1 y
slope  m 


run x2  x1 x
Or simply put
y
m
x
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Average velocity: velocity between two points on a
position time graph
Average velocity can by found graphically by finding the
slope of the line that connects the two points.
Average velocity can sometimes seem unreasonable
when the direction changes multiple times between the
two points of interest.
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Redefining the equation for slope can give us the formula
for average velocity.
rise y d d 2  d1
m



 vav
run x t
t2  t1
Or simply put
d 2  d1
vav 
t2  t1
Show units
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Instantaneous velocity: the velocity of an object at one
specific instant in time.
The instantaneous velocity can only be found graphically by
finding the slope of tangent line to a distance versus time
graph at the point of interest.
Tangent line: a line that only touches a graph once.
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Do
Transparency # 3
Instantaneous Velocity Sheet
Transparency # 4
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Velocity vs Time Graphs
If Miss. Piggy spent 3 hrs rowing her rubber canoe along the
Nile River at an average speed of 5 km/hr.
Question: What is the total distance traveled by Miss. Piggy?
15 km
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Sketch a velocity time graph which explains her trip.
Velocity
5 km/hr
Distance
3 hr
Find the area of the rectangle traced out above.
Area = length x width
5 km/hr x 3 hr = 15 km
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Question: How does the area of the rectangle compare to
the total distance traveled?
It is the same!!!
** Total distance traveled can be found from a velocity vs
time graph by calculating the area under the curve.**
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Section 2-4: Acceleration
Acceleration: The rate at which the velocity changes.
Acceleration is a vector quantity which can be in ether
positive or negative direction.
Caution: do not confuse + or – acceleration with
speeding up or slowing down.
Instead think about it as increasing in either the + or – direction.
Example: If a car is backing up and has a (-) acceleration it’s
velocity will be increasing in the negative direction.
** The car will be speeding up.**
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Constant or uniform acceleration: When the acceleration
does not change though specific time intervals.
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Non-Uniform acceleration: When the acceleration is
changing though specific time intervals.
Similar to velocity it is also possible to have both average
acceleration (between two points) as well as instantaneous
acceleration (at a single point).
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Average acceleration: acceleration between two points on
a velocity time graph
Average acceleration can be found graphically by finding
the slope of the line that connects the two points.
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Redefining the equation for slope can give us the formula
for average acceleration.
rise y v v2  v1
m



 aav
run x t t2  t1
Or simply put
v2  v1
aav 
t2  t1
Show units
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Instantaneous acceleration: the acceleration of an object at
one specific instant in time.
The instantaneous acceleration can only be found
graphically by finding the slope of tangent line to a velocity
versus time graph at the point of interest.
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Example: An airplane starts from rest, then proceeds down
the runway. If at: 10 sec it’s velocity is 30 m/s, 20 sec it’s
velocity is 60 m/s, 30 sec it’s velocity is 90 m/s. Find the
average acceleration of the airplane.
v2  v1
aav 
t2  t1
60  0 60  30
or
20  0 20  10
 3m
s
2
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Do
Go over Graph sheet
Velocity time graph work Sheet
Acceleration Conceptual Problems
Acceleration Problems
Analyzing graphs work Sheet
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Analysing Graphs Worksheet
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Do
Funny stories
Quick Quiz # 2 (Interpreting Graphs)
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Equations of Motion
So far in this chapter we have looked at three separate quantities
Distance
Velocity
Acceleration
All of which are affected by time
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As we all know from math class when you have more than one
variable you need more than one equation.
Here we have four separate variables, therefore we need four
distinct equations.
These four equations that describe motion and are called
“The equations of motion for uniform acceleration”
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Derivation of the four Equations of Motion
Equation #1
Starting from our equations for average acceleration, rearrange
and solve for final velocity
a
v f  vi
t
v f  vi  at
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Equation #2
Start by using the area under the curve of a velocity vs time
graph to find distance
1
d  vi t   v f  vi  t
2
Vf
Velocity
simplify to get
½ (vf - vi)t
Vi
1
d   v f  vi  t
2
Vi x t
Time
t
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Equation #3
Substitute #1 into #2
Eq #1  v f  vi  at
1
Eq # 2  d   v f  vi  t
2
1
d    vi  at   vi  t
2
1 2
d  vi t  at
2
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Equation #4
Rearrange # 1 for t
v f  vi  at
t
v f  vi
a
Substitute into # 2
 v f  vi 
1
d   v f  vi  

2
 a 
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Acceleration due to gravity
As long as air resistance can be ignored, acceleration due to
gravity is the same for all objects at the same location on
earth.
Acceleration due to gravity has the symbol g and it has both
magnitude and direction.
Upward is generally considered as a positive direction.
Therefore, a falling object has a negative velocity.
On the surface of the earth, a falling object generally has an
acceleration of -9.8 m/s2.
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Problem-solving strategies
1) When solving problems using orderly procedure.
2) Read the problem carefully. Try to visualize the actual
situation. Make a sketch if necessary.
3) Identify the quantities that are given in the problem.
4) Identify the quantity that is unknown, the one you have to find.
5) Select the equation or equations that will relate the given
and unknown quantities.
6) Make sure the equations can be applied to the problem, that is,
is the acceleration constant?
7)Rewrite equations as needed to solve for the unknown quantity.
8) Substitute given values including proper units into the equation
and solve. Be sure your answer is in the correct units.
9) Make a rough estimate to see if your answer is reasonable.
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Example: If a car with a velocity of 2.0 m/s at t = 0 sec,
accelerates at a rate of 4.0 m/s2 for 2.5 sec, what is its velocity at
2.5 sec?
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Example: What is the displacement of a train as it accelerated
uniformly from 11 m/s to 33 m/s in a 20.0 s time interval?
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Example: A car starting from rest accelerates uniformly at
6.1 m/s2 for 7.0 sec. How far does the car move?
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Example: An airplane must reach a velocity of 71 m/s for
takeoff. If the runway is 1.0 km long, what must the constant
acceleration be?
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Example: The time the Demon Drop ride at Cedar Point,
Ohio is freely falling is 1.5 sec.
a) What is the velocity at the end of this time?
b) How far does it fall?
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Do
Equation of motion Work Sheet
Kinematics Review Sheet
**TEST**
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