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GENERAL PHYSICS 1

Name:
Grade:
Section:
Date:

Lesson 1: Linear Motion

Learning Competencies:

 Convert a verbal description of a physical situation involving uniform acceleration in

one dimension into a mathematical description (STEM_GP12V-Ia-12)
 Interpret displacement and velocity, respectively, as areas under velocity vs. time
and acceleration vs. time curves (STEM_GP12V-Ia-14)
 Interpret a velocity and acceleration, respectively, as slopes of position vs. time and
velocity vs. time curves (STEM_GP12V-Ia-15)
 Construct a velocity vs. time and acceleration vs. time graphs, respectively,
corresponding to a given position vs. time graph and velocity vs. time graph and vice
versa (STEM_GP12V-Ia-16)
 Solve for unknown quantities in equations involving one-dimensional uniformly
accelerated motion, including free-fall (STEM_GP12V-Ia-17)
 Solve problems involving one-dimensional motion with constant acceleration in
contexts such as, but not limited to “tail-gating phenomenon”, pursuit, rocket launch,
and free-fall problems (STEM_GP12V-Ia-19)

Intended Learning Outcomes:

At the end of this Learners’ Activity Sheet, the learners are expected:
 To define kinematics, position, distance, displacement, speed, velocity, and
acceleration
 To determine the relationship between velocity and time
 To determine the relationship between velocity, acceleration, and time
 To represent graphically the linear motion of an object
 To interpret the physical quantities of linear motion represented by curves of a graph
 To solve problems involving speed, velocity, and acceleration
 To construct graphs that will represent two-dimensional motion

Introduction:

Imagine
A Bugatti Chiron Super Sport 300+ is travelling at 350 mph in track, when suddenly a
Hennessey Venom F5 travelling at 280 mph appears a mile away from it. The two are both
travelling at the same track and direction. The driver of the Bugatti slams on his brakes.
Given the brakes set capacity, will there be a crash? Will it be able to decelerate to stop
before it hits the Hennessey Venom F5?

Kinematics is a subfield of Mechanics that deals with the description of the motion of
objects using words, diagrams, numbers, graphs, and equations regardless of the source of
motion. It is the science that attempts to answer such questions as the questions above.
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Source: https://en.wikipedia.org/wiki/Modern_physics

In describing the motion of an object, it is a prerequisite to describe its position first.

Position is where an object is at in a particular time.

Think Of It
A person outside the bus might say that the bus moved away from the tree. The tree is
used here as the reference (or origin) position. The position of the bus is being compared
with respect to the position of the tree.

A person inside the bus might say that the tree moved away from the bus. The bus is
used here as the reference (or origin) position. The position of the tree is being compared
with respect to the position of the bus.

Motion is always relative. The motion of one object may be described in

reference with the position of the other object and vice versa. The only difference is the
origin or reference point used. If taken at the same time, both observations are correct.
Thus, motion may be defined as the change in position over time.

When one object moves from one place to another in a straight line it is called
translational motion. It may be described using position, distance, displacement, speed,
velocity, and acceleration.

 Distance Vs. Displacement

Distance – the total path travelled by an object; the summation of all the distances taken
from the starting point to the end point; a scalar quantity
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Displacement - the length of the straight line joining the starting point and end point where a
body has travelled; it is the shortest path to travel from the initial position to the destination; a
vector quantity.

(Blue line): distance

(Red line): displacement

Displacement Distance
-change in position -sum total of the path taken

+++…+

-
-
-
*Note: There is no negative distance.
Negative displacement means the direction is opposite your assigned positive
direction.

Example:

A cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is her
displacement? (b) What distance does she ride? (c) What is the magnitude of her
displacement?

Solutions:
(a) The rider’s displacement is Δx = xf − xi=-1 km. (The displacement is negative because we
take east to be positive and west to be negative.)
(b) The distance traveled is 3 km + 2 km = 5 km.
(c) The magnitude of the displacement is 1 km.
 Speed Vs. Velocity
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When an object is travelling along a straight line its velocity is equal to its speed.

Speed Velocity
-tells how fast an object is moving -measures how fact an object is in motion
-rate of change in distance considering its direction
-rate of change in displacement

-
-
-
-
-ex. 15
-ex. 15 , East

 Instantaneous Velocity

Instantaneous Velocity is the velocity of an object at a single time. In position vs. time
graph, it is the slope at any point on the graph.

 Average Velocity

Average Velocity is the slope generated by two points on the position vs. time graph. It
is the ratio of the difference in position over the time interval taken by such motion.

⃑ x x f  xi
vavg  
t t f  ti
Where:
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x rise
v    Slope
a.) avg
t run b.) x  v(t )  height (base)  area
Example:

 Uniform Motion

When the distances covered by an object over a constant interval of time are equal to
one another, the object is said to be in uniform motion. Thus, the speed of an object is
constant.

The distance-time graph above represents the distance travelled with respect to time.
It shows the behavior of a uniform motion. An object remaining at rest over a period of time
can also be said as having a uniform motion.

 Acceleration
Acceleration is the rate of change in velocity over a period of time, . Any change in
velocity results in acceleration – including change in direction.
 Acceleration = increasing velocity
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 Deceleration or retardation = decreasing velocity

 Centripetal acceleration = changing direction

 Instantaneous Acceleration

Instantaneous acceleration is the change of velocity from a point in time, even the
infinitely small or infinitesimal time interval, to another. It is when limits are applied. The
limit of such rate as its denominator, approaches zero is called derivative. Thus,
acceleration is the derivative of velocity.

 Constant Acceleration

The assumption here is that the acceleration near the surface of the earth, acceleration
due to gravity is approximately constant ag = 9.8 m/s2, does not change. Thus, there is a
constant acceleration.

a v
t  v  at  height (base)
0

v f  vi  a (t f  ti )

y  b  mx

x  x1  x2
x  vi t  12 t (v f  vi )
x  vi t  12 t (at )
xf = xi + v i t + 1 a t 2
2

v f  vi
x  vi t  12 at 2 t
a
   
v f  vi v f  vi 2
x  vi a  12 a a

 21a  v 2f  2v f vi  vi2 
v f vi  vi2
x  a

2ax  2v f vi  2vi2  v 2f  2v f vi  vi2

2ax  vi2  v 2f
v 2f  vi2  2ax
v 2f  vi2  2 a x

 Free-fall Motion
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When a body in motion is acted upon by gravitational force only, the body is said to
be in free-fall motion.

 Kinematics Formula

SAMPLE PROBLEMS:

1.) A particle initially at position x = 5 m at time t= 2 s moves to position x = -2 m and arrives

at time t = 4 s.
a.) Find the displacement of the particle.
b.) Find the average speed and velocity of the particle.

Solution:
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a.)
b.)

We assume that left and downward are the negative sides and right and upward are
positive sides.

2.) The straight line distance from Conestoga to Y is 97 mi. When you are traveling from
Conestoga to New York City and vice versa, the following data are obtained:
One way travel = 130 mi.
Total Distance Traveled = 260 mi. y(mi)
Travel time Con. to NY = 2.6 hrs. back
Travel time NY to Con. = 2.6 hrs. NY
up
0 Conestoga 97 x(mi)
a.) What is the average speed from Conestoga to NY?
b.) What is the average velocity from Conestoga to
NY?
c.) What is the average speed for the round trip?
d.) What is the average velocity for the round trip?

Solution:
130
a. vspeed  2.6miles  50 miles
⃑ 97 mi xˆ
hr hr

b. vavg  2.6hr  37.3 mi xˆ

hr
260miles
c. vspeed  5.2hr 50 miles
⃑
hr
0mi xˆ
d. vavg  5.2hr  0 mi
hr

3. A car reduces its velocity from 60 kph to 20 kph in 8 s. Find the acceleration in
SI.

Solution:

Initial velocity:

Final velocity:

Acceleration: or , decelerating

4. A. train maintains a constant acceleration of . What is its velocity after 6 s if its initial
velocity is due north?
Solution:
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5. A golfer sinks the putt 3 s after the ball leaves the club face. If the ball travelled with an
average speed of , how long was the putt?

Solution:

6. An airplane lands on a carrier deck with an initial velocity of and is brought to a stop in a
distance of 100 m. Find the acceleration and the stopping time.

Given:

100 m

Find: a=?
t=?

Solution:

-40.5

7. How far will a car travel in 20 s if its initial velocity is and it undergoes constant
acceleration of 2? What will be its final velocity?

Given:

t20 s

Find: x=?

Solution:

Distance:

Final velocity:

8. A rubber ball is dropped from rest. Find its velocity and position after 1, 2, 3, and 4 s.

Given:
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Find: =?

Solution:

After 1 s:

After 2 s:

After 3 s:

After 4 s:

Position:

Since initial velocity is zero, we use .

After 1 s:

After 2 s:

After 3 s:

After 4 s:

ASSESSMENT:

I. Give the needed data.

a. Distance travelled: ____________ b. Area of shaded region: ____________

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c. Acceleration: ___________________ d. Acceleration: _________________

II. Answer the following questions. Refer to the figures below.

a) List the objects below in order of increasing speed.

b) Which of the objects have positive velocity?
c) List the objects in order of increasing velocity.

III. Solve the following problems:

1. An airplane accelerates down a runway at 3 for 30 s until it finally lifts off the ground.
Determine the distance traveled before takeoff.
2. A car travelling at 22 skids to a stop in 3 s. Determine the skidding distance of the
car. (assume uniform acceleration)
3. A race car accelerates uniformly from 19 to 45 in 3 s. Determine the acceleration of
the car and the distance travelled.
4. A BMW and a Toyota Celica GT were travelling at a velocity of 110 kph with a
bumper to bumper distance of 1.5 m. After sometime, the BMW started to decelerate
at a rate of 9.8 . After the reaction time of 0.45 s, the Toyota Celica GT started to
decelerate at 9.2 . Find the safe distance between the two cars. Find the final
velocity of the Toyota Celica GT if it would hit the BMW.

References:

Tippens, P{. (2007). Physics, 7th Edition. McGraw-Hill Education, New York.

Uri Haber-Schaim {. (1976). PSSC Physics, 4th Edition Education Development Center Inc.

Ch 2. Motion in a Straight Line Definitions. Retrieved from

http://www.tesd.net/cms/lib/PA01001259/Centricity/Domain/368/ap_1_ch_2_notes_-
_annotated_a.ppt
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