Sorsogon National High School

SELF-DIRECTED LEARNING ACTIVITY SHEET IN GENERAL PHYSICS 1 (MODULE 6)

1st Quarter; School Year 2021-2022

Name of Learner: ____________________________________ Grade Level & Section: _________________

TITLE OF THE LESSON: GRAPHICAL ANALYSIS OF MOTION

I. LEARNING OBJECTIVES:
In this learning activity sheet, you will learn to interpret velocity and acceleration, respectively,
as slopes of position vs. velocity vs time curves (STEM_GP12KINIb-15) and construct 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_GP12KINIb-16).

Specifically, you should be able to:

1. Analyze motion graphs and diagrams to determine the relationships between an object’s
position, velocity, and acceleration;
2. Explain what the slope of a position vs. time graph and a velocity vs. time graph
represent; and
3. Derive velocity vs. time and acceleration vs. time graphs from a position vs. time graph
and vice versa.

II. PRESENTATION OF THE LESSON:

Graphs are used to describe real-world events. The slope of the different graphs conveys
descriptions of different physical quantities.

Position – Time Graph or Displacement – Time Graph

The slope of this type of graph describes the velocity of the object. The steeper the slope, the
faster the object moves.
These are the meaning of the shapes.

Moving away
Moving away
Slow to fast
These are three possible shapes. Constant 𝑣⃑

Moving away Moving away

Constant 𝑣⃑, slow Constant 𝑣⃑, fast

Going back Going back

Constant 𝑣⃑, slow Constant 𝑣⃑, fast

Going back Going back

NOTE: A displacement behind the reference Slow to fast Fast to slow

frame is placed in the -y. Velocity will also be

negative.

Address: Magsaysay St., Almendras-Cogon, Sorsogon City “Reach, Shine, Build a LEGACY”
Telephone No. (056)3114862
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 Velocity – Time Graph
The slope of this type of graph describes the acceleration of an object.

___________

+ direction + direction + direction + direction + direction

Increasing 𝑣⃑ Decreasing 𝑣⃑ Increasing 𝑣⃑ Decreasing 𝑣⃑ Constant 𝑣⃑
Constant 𝑎⃑ Constant 𝑎⃑ Increasing 𝑎⃑ Increasing 𝑎⃑ 𝑎⃑ = 0

NOTE: Velocity in the -y is a negative velocity which means that the object is moving in the -direction.

Acceleration – time Graph

The slope of this type of graph describes the rate of change of acceleration. This quantity is called a jerk.

Graph A shows a constant jerk and increasing 𝑎⃑

Graph B shows zero jerk and constant 𝑎⃑
Graph C shows decreasing jerk and decreasing 𝑎⃑
Graph D shows decreasing jerk and increasing 𝑎⃑

Note: A negative acceleration is placed in the -y axis. A negative

acceleration can mean that an object is moving in the opposite
direction. It can also mean that the object is slowing down (only
if the velocity is positive).

Δ𝑦 ∆𝑑 ⃑ ⃑⃑
∆𝑣
To solve for the slope, use slope= . For 𝑑⃑-t graph, the slope is 𝑣⃑= . For 𝑣⃑–t graph, the slope is 𝑎⃑= .
Δ𝑥 ∆𝑡 ∆𝑡
∆𝑎⃑⃑
And finally, for 𝑎⃑-t graph, the slope is jerk= .
∆𝑡
III. LEARNING TASKS
A. Practice Task 1: If – Then. Refer to the motion graphs below to answer the questions below.
Write all that apply.
1. If these are 𝑑⃑ − 𝑡 graphs, then which graph/s show/s the
motion of an object that is slowing down? _____________
2. If these are 𝑑⃑ − 𝑡 graphs, then which graph/s show/s an
object that is at rest?______________________________
3. If these are 𝑑⃑ − 𝑡 graphs, then which graph/s show/s an
object that has a negative acceleration?_______________
4. If these are 𝑣⃑ − 𝑡 graphs, then which graph/s show/s an
object that is at rest?______________________________
5. If these are 𝑣⃑ − 𝑡 graphs, then which graph/s show/s the
a moving object that is not accelerating?_______________
6. If these are 𝑣⃑ − 𝑡 graphs, then which graph/s show/s an
object moving to the left?___________________________
7. If these are 𝑎⃑ − 𝑡 graphs, then which graph/s show/s an
object that is at constant speed?_____________________
8. If these are 𝑎⃑ − 𝑡 graphs, then which graph/s show/s an
𝑚
object that is falling at a constant rate of -9.8 2 ?_________
𝑠
9. If graph C shows an object that has a constant 𝑎⃑, then
what kind of graph must it be?_______________________
10. If Graph F shows an object that is moving backward, then what kind of graph must it
be?_________________________________________________________________________

Address: Magsaysay St., Almendras-Cogon, Sorsogon City “Reach, Shine, Build a LEGACY”
Telephone No. (056)3114862
Email Address: 302279@deped.gov.ph/sorsogonnhs.shs@gmail.com
 B. Practice Task 2: Graphical Analysis. The graph below presents a part of the run-walk routine
of a man exercising along Sorsogon City Coastal Road. Use it in answering the questions below.

1. What is the highest speed of the man?_______________

2. At which time intervals is he momentarily at
rest?___________________________________________
3. What is his biggest acceleration? Show your
solution._________________________________________
_______________________________________________
4. How far and in what direction did he walk between 7 and
12 seconds? Show your computation._________________
_______________________________________________
_______________________________________________

IV. GENERALIZATION
Plot It! Make a position – time graph the motion of both Jack and Jill based on the nursery
rhyme below.
Jack and Jill went up the hill to fetch a pail of water. Jack fell down and broke his crown and Jill came
tumbling after.

LEGEND:

V. EVALUATION

Direction: Select the correct answer.

The velocity as a function of time of a moving object is presented by the graph to the right. Use
this graph for questions 1 and 2.

1. Describe the velocity of the object from 2-6 seconds.

a. constant speed c. increasing speed
b. decreasing speed d. not moving

2. How far from the origin does the object move in first 6 s?
a. 4 m b. 16 m c. 20 m d. 28 m

Address: Magsaysay St., Almendras-Cogon, Sorsogon City “Reach, Shine, Build a LEGACY”
Telephone No. (056)3114862
Email Address: 302279@deped.gov.ph/sorsogonnhs.shs@gmail.com
 3. A cheetah chases a gazelle, reaching a speed of 28m/s. A graph of its
acceleration over time is shown, where rightward is the positive
acceleration direction.

Which graph shows the cheetah's velocity over time?

a. Dog dog b. c. d.

4. Justin drives west at 20 m/s then slows to a stop at the red light. A graph of
his acceleration over time is shown below, where eastward is the positive
acceleration direction.

Which graph shows his velocity over time?

a. b. c. d.

5. Describe the object whose motion is shown in the v-t graph.

a. The object is slowing down at t = 2s.

b. The object is speeding up at t = 2s.
c. The object is moving forward.
d. The object is moving backward.

References:
Duka, Roderico D. “General Physics 1 Quarter 1 Module 5: Describing Motion.”
Labayandoy, Lope. “General Physics 1 Quarter 1 Module 6: Graphical Analysis of Motion.”
https://kids.britannica.com/kids/article/motion/399909
https://courses.lumenlearning.com/physics/chapter/3-2-vector-addition-and-subtraction-graphical-methods/
https://www.physicsclassroom.com/class/1DKin/Lesson-1/Distance-and-Displacement

VI. REMARKS:
In this part, you can tell your teacher what confused you, what part did you find difficult or what
you learned about.
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________

Prepared by RACHEL D. LEE, Teacher III

Address: Magsaysay St., Almendras-Cogon, Sorsogon City “Reach, Shine, Build a LEGACY”
Telephone No. (056)3114862
Email Address: 302279@deped.gov.ph/sorsogonnhs.shs@gmail.com