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SCIENCE
Third Quarter – Module
1 Describing Motion

Department of Education ● Republic of the Philippines

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 Lesson
Distance and Displacement
1

About two centuries ago, people used animals like horses and donkeys
to transport people and goods. In 1860, the internal combustion engine was
developed by Nicolaus Otto that led the way to the invention of motor cars,
trains, ships, airplanes and jets which enabled people to travel faster. All of
these involved motion.

What’s In

Activity 1: Sketch It
Directions: Copy figure 1 completely in a graphing paper. Consider the center
of your graphing paper as the reference point. Sketch the four vector
quantities in one graphing paper following the given example. Paste
your graphing paper in your Science activity notebook.

North
Example:
6 meters East

1. 8 meters East West

C East
2. 10 meters North
3. 12 meters West
4. 14 meters South

0 1 2 34 5 6 7 8 9
South

Figure 1. Graph

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 What’s New

Motion is the change in position with respect to the reference point. An

object is said to be moving when it has traveled a certain distance or
displaced from a point of reference. Describing the point of reference and its
direction will be learned by performing activity 2.

Activity 2: My Road Map

Directions: Below is a road map showing two routes from home to school.
Which route will you choose and why? Write your answers in your
Science activity notebook.

SCHOOL
HOME

Figure 2. Road Map

What Is It

Motion is the change in position for a particular time interval. If a body

has changed its position, we can say that it has moved with respect to its
original position. Thus, the original position serves as the reference point.

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 An object may be moving with respect to another reference. For
example, when you are inside a bus, you are not moving with respect to the
other passengers, but you are moving with respect to the ground.
Motion can be described by measuring the total length of the path
travelled by the object, and by measuring the distance between the initial
position and final position of the
object.

Example:
A car ran 100 meters from
point A to point B, then 50 meters
from point B to point C, and
another 100 meters from point C
Figure 3: Distance travelled
to point D. See Figure 3 and 4.
To solve the total length of path travelled you can simply add the length
of path from point A to B, B to C and C to D.
Total length of path = length A to B + length B to C + length C to D.
= 100 meters + 50 meters + 100
meters Total length of path = 250 meters

The length of the entire path that the object travelled is referred to as
distance. Based on the example above, the total length of path is equal to 250
meters. This means that the distance travelled by the car is equal to 250 meters.
Displacement is the
shortest distance between the
object’s initial and final positions as
shown in Figure 4.
To solve the displacement of
the car, simply subtract the final
position by the initial position.
Figure 4. Displacement
Displacement = Final position – Initial position
= 50 meters – 0
Displacement = 50 meters

Distance is a scalar quantity, it has magnitude but no direction while

displacement is a vector quantity that has both magnitude and direction.

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 What’s More

Activity 3: My Travel
Directions: Trace the distance and displacement using the figure below.
Answer the following questions in your Science activity notebook.
Situation:
You are told to buy some foods in the market. You walked 12 m East
from home, 12 m North, 6 m West, 6 m South, 6 m West, and finally, 8 m
North to reach the market.

Figure 5. Road Map

1. What is your total distance travelled?

2. Do you have a displacement?
3. What is your displacement?
4. How did you determine the distance and displacement?

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 Lesson
Speed and Velocity
2

In the previous lesson, distance and displacement were used to

describe motion of objects. This lesson gives you another way of describing
motion of objects in terms of speed and velocity.

What’s In

Activity 1: True or False

Directions: In your Science activity notebook, write T if the statement is
TRUE and F if the statement is FALSE.
1. Kilogram is a unit for distance.
2. The quantity 2 meters is a distance.
3. The quantity 2 kilometers is a displacement.
4. The quantity 2 meters to the left is a distance.
5. The quantity 2 meters to the left is a displacement.
6. Distance is the length of the entire path travelled by an object.
7. Displacement includes both distance and direction of the object’s
position.
8. The displacement is equal to zero when an object’s initial and final
position is the same.
9. The shortest distance between the initial and final position of the object
is called displacement.
10. The total distance travelled of an object from its initial position to a
certain position and back to its initial position is zero.

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 What’s New

Activity 2: Who Walks Faster?

Directions: Read the text inside the box then answer the questions below to
help John and Mary determine who walks faster. Write your
answers in your Science activity notebook.

Just yesterday John and Mary were given assignments to

record the measured distance and time spent in walking from their
home to the school.
John’s home is 400 meters while Mary is 200 meters away
from the school. It took 400 seconds for John while Mary needed
200 seconds to reach the school.

200 m
400 m
Figure 6. Distance from Home to School

1. Compare how fast John walked than Mary.

2. What is the basis of your answer in number 1?

What is it?

Speed and Velocity

Speed is the rate of distance covered at a given time.
= ; in symbols, =

We can express speed in terms of miles per hour (mi/h), kilometers per
hour (km/h), or meters per second (m/s).

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 Examples:

Solving for Mary’s speed: Solving for John’s speed:

Given: Given:
d = 200 m d = 400 m
t = 200 s t = 400 s
Asked: Asked:
=? =?

Formula: Formula:

= =

Solution: Solution:

= =

200 400

= = 400
200

= / = /

Therefore, John is as fast as Mary. Both have the same speed

of 1 meter per second (1 m/s).
When a direction is associated with speed, it refers to the quantity
known as velocity. Thus, velocity is a speed in a given direction.
Since velocity has direction it uses displacement instead of distance.

Figure 7a. Distance Figure 7b. Displacement

= ; in symbols,

As shown in Figure 7a, the total distance from home to school is 3.0
km while the displacement is 2.0 km, East as shown in Figure 7b.
Suppose you take 0.5 hour to travel from home to school, use the
information in Figure 7a and 7b to solve for your average speed and velocity.

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 Solving for average speed: Solving for average velocity:
Given: Given:
d = 3.0 km
= 2.0 km
t = 0.5 h t = 0.5 h
Asked: Asked:
=?

Formula: Formula:
=

Solution: Solution:

3.0
= 2.0 ,
0.5 ℎ

0.5 ℎ

= . /
= . / , East

A change in velocity happens when there is a change in:

A. Magnitude (speed)
Example: 60 km/h, North to 40 km/h, North
B. Direction of motion
Example: 60 km/h, North to 60 km/h, South
C. Both magnitude and direction
Example: 60 km/h, North to 40 km/h, South

Average and Instantaneous Speed

Average speed is the total distance travelled divided by the total time of
travel. Instantaneous speed is the speed at an instant in time.

A vehicle has a speedometer that tells you the

speed at that instant or at that moment in time. As the
vehicle travels along a busy street, you will notice that
the speedometer may read 30 km/h. It may change Figure 8. Speedometer

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 speed to 65 km/h as it passes an open free highway and zero when it stops.
During the entire trip, the vehicle travels at different speed.

Average and Instantaneous Velocity

When you ride a vehicle it is not only the speed that changes but also its
direction. A vehicle may travel North, West, East or South. Average velocity
is the total displacement (final position - initial position) travelled divided by
the total time of travel. Instantaneous velocity is the velocity of an object at
an instant time.
Constant Motion
Constant motion refers to an object moving with constant speed or
constant velocity. To have a constant velocity, both speed and direction
must be the same.
Example: A car running at a speed of 50 km/h all throughout its travel in a straight lin

Lesson:Acceleration
In this lesson, you will learn to describe the motion of an object in which velocity
changes in magnitude, direction, or both.

What’s In
Activity 1: Speed or Velocity
Directions: Determine the following quantities whether it is speed or velocity.
Write your answers in your Science activity notebook.

Table 1. Speed or Velocity

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 What’s New

Activity 2: Read Me!

Directions: The figure below shows the car’s speedometer reading with
respect to time. Get the speedometer’s reading of the car’s
speed from 00:00 to 00:04 s. Write your answers in your
Science activity notebook.

00:00 00:01 s

00:02 s 00:03 s 00:04 s

Figure 9. Speedometer Readi

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SUMMATIVE TEST 1

Directions: Complete the paragraph by filling in the blanks using the correct
word/s from the box. Write your answers in your Science activity
notebook.
acceleration displacement position
average distance scalar
constant deceleration speedometer
direction motion velocity
Motion is a change in (1.) __________ with respect to a reference point.
Distance and displacement, speed and velocity, and acceleration are ways to
describe motion. Distance is a (2.) ________ quantity having magnitude but no
direction while (3.) __________ is a vector quantity having both magnitude and
direction. (4.) __________ speed refers to the total distance travelled divided
by the total time and (5.) __________ is displacement divided by total time of
travel. A (6.)__________ measures instantaneous speed/velocity.
(7.)________ motion refers to an object moving with constant speed or constant
velocity. (8.) __________ is defined as the change in velocity in a time interval.
Acceleration may change in any of the following conditions: when the velocity
changes, when the (9.)__________ of motion changes, or when both velocity
and direction of motion changes. (10.) __________ is the opposite of
acceleration where the velocity of an object decreases.

What I Can Do
Directions: Copy and complete the table by solving the missing values of the
quantities. Write your answers in your Science activity notebook.

Initial Velocity Final Velocity Time (∆t) Acceleration

Balls
2
(m/s) (m/s) (s) (m/s )
1 10 20 2

2 20 70 5

3 50 30 10

4 15 30 3

5 12 12 2
\

Directions: Choose the letter of your answer and write it in your Science
activity notebook.

1. It is a continuous change in position of an object with respect to a

reference point.
A. At rest B. Magnitude C. Motion D. Reference
2. When is an object considered to be in motion?
I. When its position changes with respect to a point of reference.
II. When its distance changes with respect to a point of reference.
III. When its direction changes with respect to a point of reference.
IV. When its speed changes with respect to a point of reference.
A. I only B. I and II only C. I, II and III D. I, II, III and IV
3. Which of the following is true about an object that travels 5 meters to
the left, then 2 meters up, then another 5 meters to the right?
A. Displacement of the object is equal to 12 meters.
B. Displacement of the object is equal to 12 meters down.
C. Total distance travelled by the object is equal to 12 meters.
D. Total distance travelled by the object is equal to 12 meters down.
4. This refers to the speed of an object at a specific moment in time.

A. Average Speed C. Instantaneous Speed B. Constant Speed

D. Zero Speed
5. If a person runs 100 meters in 10 seconds, what is his average speed?
A. 2 m/s B. 5 m/s C. 10 m/s D. 20 m/s
6. A car traveling in a circle has changing velocity because it is_____.
A. not traveling at a constant speed
B. not traveling in a constant direction
C. traveling too slowly to measure its velocity
D. traveling in a constant direction at a constant speed

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7. From home, Dong walked 300 m East to visit Inday. Both Dong and
Inday walked another 400 m North and 300 m West. Which of the
following statements is NOT TRUE?
A. Dong went home.
B. Dong travelled a total distance of 1,000 m.
C. Dong’s displacement is zero if they continue to travel 400 m South.
D. Dong’s displacement is shorter than the total distance he has
travelled.
8. Which of the following statements is TRUE?
I. The distance travelled by an object can be equaled to its
displacement.
II. The displacement of a moving object can be greater than its
distance travelled.
III. The displacement of a moving object is lesser than its
distance travelled.
A. I and II B. II and III C. I and III D. I, II and III
9. This refers to the rate of change in velocity of an object.
A. Acceleration B. Motion C. Speed D. Velocity
10. Two boys walked a 200-meter distance path. It takes 5 minutes for Boy A
to finish while 10 minutes for Boy B. How do you compare their speed?
A. Boy B is faster than Boy A C. They have the same speed
B. Boy A is slower than Boy B D. Boy A is twice faster than Boy B
11. Which of the following statements is correct about an object moving in
a constant motion?

I. It moves with unchanging speed.

II. It moves with a changing velocity.
III. Its location and arrival is easy to predict.
IV. Its instantaneous speed values are always the same.

A. I, II, III B. I, II, IV C. I, III, IV D. II, III, IV

12. Which of the following is the unit of acceleration?
2
A. m/h B. m/mi C. m/s D. m/s

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13. Which of the following situations show that the object is accelerating?

I. A truck changing directions

II. A car speeding up in a high way
III. A moving motorcycle comes to stop
IV. A rolling ball moving with a uniform speed

A. I and II B. I and III C. I, II and III D. I, II, III and IV

14. The table shows the velocity of the car per unit time.
Time (hour) 0 1 2 3 4 5
Velocity (kilometer per hour) 0 20 20 60 80 0

Which of the following statements is TRUE? A.

The car is decelerating between 4-5 hours. B.
The car is accelerating between 1-2 hours.
C. The car returns to its original position after 5 hours.
D. The acceleration of the car from 2-3 hours and 3-4 hours are the
same.
15. Refers to acceleration where a moving object slows down before it stops.
A. Average acceleration C. Deceleration
B. Constant acceleration D. Instantaneous acceleration

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