Physics
05/26/2020
1-D Kinematics (Describing Motion in Words)
Chapter #1
Lesson #1
[SUBJECT]
UPCAT Reviewer – Science Subtest
OUTLINE
I.
II.
Physics
Language of Physics
A. Mechanics
B. Kinetics
III. [SUBJECT]
Scalars and Vectors
A. Scalars
B. Vectors
IV. Distance and Displacement
A. Distance
[SUBJECT]
B. Displacement
MM/DD/YYYY
Speed and Velocity
A. Speed Shifting #
Trans #
B. Velocity
VI. Acceleration
A. General Principle
B. Additional Topic
C. Nice-To-Know
Information
VII. Review Questions
VIII. References
V.
I. PHYSICS
 Major science that deals with the fundamental constituents of
the universe, the forces they exert on one another, and the
results produced by these forces
 Study of matter, force, energy and motion that helps explain
how and why matter moves through space and time
 Basically a mathematical science wherein principles and
phenomena are explained in mathematical quantities and
mathematical relationship
II. LANGUAGE OF PHYSICS
Diagram 1: Branches of Physics
Physics
Mechanics
Kinematics
Optics
Electricity
B. VECTORS
 Quantities that are fully described by a magnitude and a
direction
 Displacement
(m)
 Velocity
(m/s)
 Acceleration
(m/s2)
 Force
(N)
 An arrow is used to represent a vector
 Arrowhead
 Indicates the direction of the vector
 Length of the arrow
 Represents the magnitude of the vector
 Tail
 Represents the origin of the vector
IV. DISTANCE AND DISPLACEMENT
 Distance and displacement are two quantities that may seem to
mean the same thing yet have distinctly different definitions and
meanings
A. DISTANCE
 Scalar quantity
 Refers to “how much ground an object has covered” during its
motion
 Defined to be the magnitude or size of displacement between
two positions
 Distance between two positions is not the same as the distance
traveled between them
 Distance traveled
 Total length of the path traveled between two positions
Heat
Dynamics




B. DISPLACEMENT
Vector quantity
Refers to “how far out of place an object is”
Object’s overall change in position
Net distance moved or net change in position
Formula 1: Displacement
A. MECHANICS
 Branch of Physics concerning the motions of objects and their
responses to forces
 Careful definition of such quantities as displacement (distance),
time, velocity, acceleration, mass, and force
 Can be divided into two areas
 Kinematics
 Dynamics
B. KINEMATICS
 Branch of Mechanics
 Science of describing the motion of objects using words,
diagrams, numbers, graphs, equations
 Study of motion without considering its causes
III. SCALARS AND VECTORS
A. SCALARS
 Quantities that are fully described by a magnitude (or numerical
value) alone
 Time
(s)
 Distance
(m)
 Speed
(m/s)
 Work
(J)
 Energy
(J)
 A scalar can be a negative
 The minus sign indicates a point on a scale
 Scalars are never represented by arrows
UPCAT-Sci
Physics
∆𝒙 = 𝒙𝒇 − 𝒙𝟎
Wherein:
∆𝑥 = displacement
𝑥𝑓 = final position
𝑥0 = initial position
V. SPEED AND VELOCITY
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






A. SPEED
Scalar quantity
Refers to “how fast an object is moving”
Can be thought as the rate at which an object covers distance
Rate position changes
Rate distance is covered
An object with no movement at all has a zero speed
Does not keep track of direction
Two kinds
 Average speed
 The average of all instantaneous speeds
 Found simple by a distance/time ratio
 Units of speed
 m/s
 km/h
 mi/h
Formula 2: Average Speed
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒔𝒑𝒆𝒆𝒅 =
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒆𝒅
𝒕𝒊𝒎𝒆 𝒐𝒇 𝒕𝒓𝒂𝒗𝒆𝒍
 Instantaneous speed
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 The speed at any given instant time
 What the speedometer says
 Not measured over a time interval, like average speed
Formula 3: Instantaneous Speed
∆𝒙
𝒙𝟐 − 𝒙𝟏
𝒊𝒏𝒔𝒕𝒂𝒏𝒕𝒂𝒏𝒆𝒐𝒖𝒔 𝒔𝒑𝒆𝒆𝒅 =
=
∆𝒕
𝒕𝟐 − 𝒕𝟏
Wherein:
∆𝑥 = change in distance
∆𝑡 = change in time
 Constant speed
 If the instantaneous speed has always the same value
 Average speed = Instantaneous speed
Table 1: Objects with constant and changing speed
Constant Speed (6 m/s)
Time (s)
Position (m)
0
0
1
6
2
12
3
18
4
24
Changing Speed
Time (s)
Position (m)
0
0
1
1
2
4
3
9
4
16
B. VELOCITY






Vector quantity
Refers to “the rate at which an object changes its position”
Velocity = speed + direction
How fast its position is changing
Direction aware
Direction of velocity is simply the same as the direction that an
object is moving
 Two kinds
 Average velocity
 The average of all instantaneous velocities
Formula 4: Average Velocity
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 =
𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕
𝒕𝒊𝒎𝒆
 Instantaneous velocity
 Average velocity at a specific instant in time
VI. ACCELERATION




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



Vector quantity
Defined as the rate at which an object changes its velocity
An object is accelerating if it is changing its velocity
Has to do with changing how fast an object is moving
If an object is not changing its velocity, then it is not
accelerating
The greater the acceleration, the greater the change in velocity
over a given time
Direction of the acceleration vector depends on two things
 Whether the object is speeding up or slowing down
 Whether the object is moving in the + or - direction
Deceleration
 When an object slows, its acceleration is opposite to the
direction of its motion
Two kinds
 Average acceleration
 Ratio of change in velocity per unit time
 Rate of which velocity changes
Formula 5: Average acceleration
𝒂𝒂𝒗𝒆 =
𝒗𝒇 − 𝒗𝒊
𝒕
Wherein:
𝑎𝑎𝑣𝑒 = average acceleration
𝑣𝑓 = final velocity
𝑣𝑖 = initial velocity
𝑡 = time interval
 Instantaneous acceleration
 The change in velocity at any given time
 Acceleration
 Constant acceleration
UPCAT-Sci
Physics: 1-D Kinematics
 Average acceleration = Instantaneous acceleration
Table 2: Motions of objects with a constant acceleration and a changing
acceleration
Constant Amount
Time (s)
Velocity (m/s)
0
0
1
4
2
8
3
12
4
16
Changing Amount
Time (s)
Velocity (m/s)
0
0
1
1
2
4
3
5
4
7
A. GENERAL PRINCIPLE
 If an object is slowing down, then its acceleration is in the
opposite direction of its motion
 Can be applied to determine whether the sign of the
acceleration of an object is positive or negative, right or left, up
or down, etc.
 Positive acceleration
 When an object is speeding up, the acceleration is in the
same direction as the velocity
Table 3: Examples of positive acceleration
Example A
Example B
Time (s)
Velocity (m/s)
Time (s)
Velocity (m/s)
0
0
0
-8
1
2
1
-6
2
4
2
-4
3
6
3
-2
4
8
4
0
 In example B, the object is moving in negative direction and
is slowing down. Looking at the general principle, this
example is also a positive acceleration
 Negative acceleration
 When an object is slowing down, the acceleration is in the
opposite direction as the velocity
Table 4: Examples of negative acceleration
Example C
Example D
Time (s)
Velocity (m/s)
Time (s)
Velocity (m/s)
0
8
0
0
1
6
1
-2
2
4
2
-4
3
2
3
-6
4
0
4
-8
 In example D, the object is moving in a negative direction
and is speeding up. Looking at the general principle, this
example is also a negative acceleration.
B. ADDITIONAL TOPIC
 Since accelerating objects are constantly changing their
velocity, one can say that the distance traveled/time is not a
constant value
 Free-falling objects
 Usually accelerates as it falls
Time
Velocity
Ave.
Distance
Total
interval
change
velocity
traveled
distance
during
during
during
traveled
interval
interval
interval
from 0s
to end of
interval
0 – 1.0s
0 - ~10m/s
~5m/s
~5m
~5m
1.0 – 2.0s ~10 – 20m/s
~15m/s
~15m
~20m
2.0 – 3.0s ~20 – 30m/s
~25m/s
~25m
~45m
3.0 – 4.0s ~30 – 40m/s
~35m/s
~35m
~80m
 Observe that the object averages a velocity of approximately
5 m/s in the first second, approximately 15 m/s in the second
second, approximately 25 m/s in the third second,
approximately 35 m/s in the fourth second, etc. Our freefalling object would be constantly accelerating.
 Given these average velocity values during each consecutive
1-second time interval, we could say that the object would
fall 5 meters in the first second, 15 meters in the second
second (for a total distance of 20 meters), etc.
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 Free-fall
 Motion under the influence of gravity only
 No friction or air resistance
 Acceleration of an object in free fall is constant
 Free-fall acceleration: about 10 m/s2 or 9.8 m/s2 (32 ft/s2
or 22mi/hr/s in English units)
6. Use the diagram in number 2 to determine the average
speed and the average velocity of the skier during these three
minutes.
C. NICE-TO-KNOW INFORMATION
If an object is changing its velocity - whether by a constant amount
or a varying amount - then it is an accelerating object. And an
object with a constant velocity is not accelerating.
7. Use the diagram in number 3 to compute for the coach’s
average speed and velocity.
Positive and negative describes direction
The effect of air resistance is to slow an object down and/or
decrease its acceleration
VII. REVIEW QUESTIONS
1. Identify whether the following quantities are scalar or vector
quantities.
a. 5m
b. 30m/sec, East
c. 5mi., North
d. 20 degrees Celsius
e. 256 bytes
f. 4000 calories
2. Use the diagram to determine the resulting displacement
and the distance traveled by the skier during these 3
minutes.
8. Consider the following problems and the corresponding
solutions. Use the equation for acceleration to determine the
acceleration for the following two motions.
Practice A
Time (s)
Velocity (m/s)
0
0
1
2
2
4
3
6
4
8
Practice B
Time (s)
Velocity (m/s)
0
8
1
6
2
4
3
2
4
0
VIII. REFERENCES
3. What is the coach’s resulting displacement and distance of
travel?
Academic Clinic (2011). Science readings 4. Retrieved from http://academicclinic.com/wp-content/uploads/2011/05/Science-Readings-4.pdf.
Espana, R., Gerona, Z., Salmorin, L., Villamil, A. (2003). Science and
technology physics (updated edition). Quezon City: Abiva Publishing
House, Inc.
Physics
Classroom
(2020).
Acceleration.
Retrieved
from
https://www.physicsclassroom.com/class/1DKin/Lesson-1/Acceleration.
Physics Classroom (2020). Distance and displacement. Retrieved from
https://www.physicsclassroom.com/class/1DKin/Lesson-1/Distance-andDisplacement.
Physics
Classroom
(2020).
Introduction.
Retrieved
from
https://www.physicsclassroom.com/class/1DKin/Lesson-1/Introduction.
Physics Classroom (2020). Scalars and vectors. Retrieved from
https://www.physicsclassroom.com/class/1DKin/Lesson-1/Scalars-andVectors.
Physics Classroom (2020). Speed and velocity. Retrieved from
https://www.physicsclassroom.com/class/1DKin/Lesson-1/Speed-andVelocity.
Stanbrough,
J.
(2008).
Kinematics.
Retrieved
from
http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Kinematics/kine
_in_a_nutshell.htm.
Vea, M., & Espiritu, M. (2007). UPCAT reviewer (revised edition). Quezon City:
V.E.A Learning, Inc.
4. What is the displacement of the cross-country team if they
begin at the school, run 10 miles and finish back at the
school?
5. What is the distance and the displacement of the race car
drivers in the Indy 500?
UPCAT-Sci
Physics: 1-D Kinematics
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