PHYSICS
Unit 1 Kinematics (1-D motion in a straight line)
Notes
I.
Describing motion with words- The motion of objects
can be described by words, such as distance,
displacement, speed, velocity, and acceleration. These
mathematical quantities that are used to describe the
motion of objects can be divided into two categories.
A. The quantity is either a vector or a scalar. These two
categories can be distinguished from one another by
their distinct definitions:


Scalars are quantities which are fully
described by a magnitude (how big or small)
alone.
Vectors are quantities which are fully
described by both a magnitude and a direction.
B. Distance and displacement are two quantities that
may seem to mean the same thing, yet they have
distinctly different meanings and definitions.


II.
Distance is a scalar quantity which refers to
"how much ground an object has covered"
during its motion.
Displacement is a vector quantity which
refers to "how far out of place an object is"; it
is the object's change in position.
Speed- measure of how fast something moves,
measured by a unit of distance divided by a unit of time.
distance
time

speed =

Any combination of distance and time units is
legitimate for measuring speed.
speed is a scalar quantity
speed is also relative, it depends on your frame
of reference.


A. Instantaneous speed- the speed at any particular instant
in time. Think of a speedometer on a car
B. Average speed- The average speed of an object tells you
the (average) rate at which it covers distance. If a car's
average speed is 65 miles per hour, this means that the
car's position will change (on average) by 65 miles each
hour.

Average speed is a rate. In kinematics, a rate
is always a quantity divided by the time taken
to get that quantity (the elapsed time). Since
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

average speed is the rate position changes,
average speed = distance traveled/time taken.
speedave. =
distance
time
C. Constant speed- Moving objects don't always travel
with erratic and changing speeds.

Occasionally, an object will move at a steady
rate with a constant speed. That is, the object
will cover the same distance every regular
interval of time.
Equal distances are covered in equal time
intervals.

III.
Velocity- in physics we distinguish between
speed and velocity.
 velocity is speed in a given direction, north, left,
right, up, etc.




IV.
we also distinguish between average, constant
and instantaneous velocity as we do for speed.
constant velocity means constant speed with no
change in direction.
velocity is a vector quantity
Acceleration- We can change the velocity of
something by changing its speed, changing its
direction, or by changing both its speed and its
direction.
A.
How quickly velocity changes is
acceleration.

B.

Suppose we are driving and in 1 sec. we
steadily increase our velocity from 30 km/h to
35 km/h, and then to 40 km/h, and so on.

We change our velocity by 5 km/h each second,
acceleration = 5 km/h  1 sec.

Note that a unit of time enter twice.
Acceleration is not just the total change in
velocity; it is the time rate of change, or change
per second.
Free fall-A free-falling object is an object that is
falling under the sole influence of gravity. Thus, any
object that is moving and being acted upon only by
the force of gravity is said to be "in a state of free
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fall." This definition of free fall leads to two important
characteristics about a free-falling object:
1.
Free-falling objects do not encounter air
resistance.
2. All free-falling objects (on Earth)
accelerate downwards at a rate of
approximately 10 m/s/s (to be exact, 9.8
m/s/s).
C.
How fast- The velocity of a free-falling object
which has been dropped from a position of rest is
dependent upon the length of time for which it has
fallen. The formula for determining the velocity of a
falling object after a time of t seconds is:


V f = Vi + a × t
Vi is the initial velocity of the object.
D. How far- The distance which a free-falling object has
fallen from a position of rest is also dependent upon the
time of fall. The distance fallen after a time of t seconds
is given by the formula below:
1
d = v i t + at 2
2

V.
Describing motion with diagrams.
A. “Ticker tape” diagram. The trail of dots provides a
history of the object's motion and therefore a
representation of the object's motion.
1.
2.
3.
Distance between dots represents position
change in that time interval.
A changing distance between dots shows a
changing velocity and thus an acceleration.
A constant distance between dots represents a
constant velocity and therefore no acceleration.
B. Vector diagram. They depict the direction and
relative magnitude of a vector quantity by a vector
arrow.
1.
2.
The magnitude of a vector quantity is represented
by the size of the vector arrow.
Direction is shown by direction the arrow is
pointing.
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VI.
Describing motion with graphs.
B. Position vs. Time graphs. Graphing onedimensional motion.
1.
If the velocity is constant, then the slope is constant
(i.e., a straight line).
2.
If the velocity is changing, then the slope is
changing (i.e., a curved line).
3.
If the velocity is positive, then the slope is positive
(i.e., moving upwards and to the right).
4.
If the velocity is negative, then the slope is negative
(moving downward to the right).
B. Velocity vs. Time graphs.
1.
If the velocity is constant, then the slope is zero (i.e.,
a straight line).
2.
If the velocity is changing, then the slope is
constant.
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C. In summary, the three types of graphs are
 d vs. t,
 v vs. t, and
 a vs. t
1.
Constant velocity graphs.
d
v
a
t
2.
t
t
Constant acceleration graphs (a > 0)
d
v
a
t
3.
t
t
Graphs are related

Graphing the slopes generates the graph to the right


Determining the area under the graph to the right
generates the graph to the left
triangle= ½ bh
rectangle= bh
trapezoid= ½ b(h1+h2)
VII. Vectors
A. Vectors and Scalars- arrows are used to symbolize
a vector. Used to illustrate vector quantities like
velocity, acceleration, force, etc. Scalars only
represent magnitude; such as time, speed, distance.
1.
2.
3.
arrow points in the direction of the vector
magnitude is the length of the vector.
positive x-axis is referenced as 0.
B. Addition of vectors- tail to tip method, vectors are
laid out tail to tip, the sum (R = resultant) equals the
length and angle of the line that connects the tail of
the first vector to the tip of the last vector.
B
R=A+B
A
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
C. Addition of vectors- component method
What is the resultant velocity of the
motor boat?
An x-y coordinate system is established and  is
measured counterclockwise from +x axis (0).

y=90
B
B
A
A
X=0

x-component and y-component for each vector are
calculated (R = magnitude;  = direction)
cos = adjacent
hypotenuse
sin = opposite
Rx= Rcos
Ry= Rsin
hypotenuse
Rx=Ax+ Bx
y=90
Bx=BcosB
By=BsinB
Ry=Ay + By
B
A
Ay=AsinA
Ax=AcosA
VIII.



Ax + Bx = Rx
Ay + By = Ry
R = Rx 2 + Ry 2

tan  =
X=0
R
Ry
q = tan-1 y
Rx
Rx
Relative Velocity and Riverboat problemsA. On occasion objects move within a medium that is
moving with respect to an observer.

a plane flying into the wind

a motorboat moving across a river
1.
2.
Problems such as these can be solved using the
aforementioned trigometric functions.
Motorboat type problems are usually accompanied
by three separate questions:
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 if the width of the river is X meters wide, then
how much time does it take the boat to travel
shore to shore?
 What distance downstream does the boat reach
the opposite shore?
IX.
Projectile Motion1. Occurs when an object is moving horizontally at a
constant velocity and vertically with an acceleration
due to gravity of -9.8 m/s2.
2. The horizontal motion is completely independent of
the vertical motion.
3.
Direction
vertical
horizontal
Solving projectile motion problems.
a) determine x-component and y-component of
initial velocity. This will be vyi and vxi
b) complete the vertical row in the data chart for
all values in the vertical direction, remember
() is negative.
c) complete the horizontal row in the data chart for
all values in the horizontal direction (vix=vfx)
d) time is the same for y and x directions
disp.
vinitial
vfinal
a
t
-9.8 m/s2
e)
f)
dy=viy+½at2
no vfy
4.
solve for unknown in the x direction with
dx=vixt
solve for the unkown in the y direction with
vfy=viy +at
vfy2=viy2 + 2ady
no dy
no t
Helpful shortcuts. When a ball is kicked at ground
level across a horizontal field.
g) viy = -vfy when ball hits the ground
h) vfy= 0 when ball reaches its highest point.
i) It takes half the time to reach its highest point.
SUMMARY OF LINEAR MOTION EQUATIONS
a=
v f - vi
t
1
d = v i t + at 2
2
vi + v f
d=
t
2
v f = v i + at
v f 2 = v i 2 + 2ad
_
v=
disp.
t
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