1. Re p u b li c o f t he P hi li ppi ne s
D e pa r t me nt o f E d uc a t i o n
Re g i o n V II , Ce nt r a l Vi s a ya s
D i vi s i o n o f M a nd a ue Ci t y
Labogon, Mandaue City
SPEED AND VELOCITY
Prepared by:
RHONNEL M. ALBURO
IV - Galatia
Visit my website: http://www.alfore.info/ to see my collection of
school related works!

2. I. Title Page
II. Table of Contents
III. Guide Card
IV. Introduction
V. Activity Card #1
VI. Activity Card #2
VII. Assessment Card #1
VIII. Assessment Card #2
IX. Enrichment Card #1
X. Enrichment Card #2
XI. Enrichment Card #3
XII. Answer Card
XIII. Reference Card

3. Hello! I am Mr. Sim. Welcome to another fun-filled
adventure as we take another journey to the world of
Physics. This time we will be talking about Speed and
Velocity. So fasten your seatbelt as we go and learn!
This Strategic Intervention Material is designed to give the learner better
understanding on the different concepts related to speed and velocity. Upon finishing
this SIM the reader is expected to:
• Define speed and velocity.
• Identify and understand the key concepts on speed and velocity.
• Differentiate Instantaneous Speed and Average Speed
• Differentiate Instantaneous Velocity and Average Velocity
• Plot the movement of an object to determine its average speed and velocity
• Solve problems related to speed and velocity.
Now that you know what you will be learning, let’s take a little review about the
topic.

4. Just as distance and displacement have distinctly different meanings (despite
their similarities), so do speed and velocity. Speed is a scalar quantity which refers to
"how fast an object is moving." Speed can be thought of as the rate at which an object
covers distance. A fast-moving object has a high speed and covers a relatively large
distance in a short amount of time. A slow-moving object has a low speed and covers
a relatively small amount of distance in a short amount of time.
Velocity is a vector quantity which refers to "the rate at which an object changes
its position." If a person in motion wishes to maximize their velocity, then that person
must make every effort to maximize the amount that they are displaced from their
original position. Every step must go into moving that person further from where he
or she started.
Velocity is a vector quantity. As such, velocity is direction aware. When
evaluating the velocity of an object, one must keep track of direction. It would not be
enough to say that an object has a velocity of 55 mi/hr. One must include direction
information in order to fully describe the velocity of the object. For instance, you
must describe an object's velocity as being 55 mi/hr, east. This is one of the essential
differences between speed and velocity. Speed is a scalar quantity and does not keep
track of direction; velocity is a vector quantity and is direction aware.
The task of describing the direction of the velocity
vector is easy. The direction of the velocity vector is simply
the same as the direction which an object is moving. It
would not matter whether the object is speeding up or
slowing down. If an object is moving rightwards, then its
velocity is described as being rightwards. If an object is
moving downwards, then its velocity is described as being
downwards. So an airplane moving towards the west with a
speed of 300 mi/hr has a velocity of 300 mi/hr, west.
Note that speed has no direction (it is a scalar) and velocity
at any instant is simply the speed with a direction.
Now you are ready to perform the coming activities.
Good Luck!

5. Activity #1
Test I. Ranking Speed
Given are four objects with varying speed. Convert the speed of each object to the desired unit
22
and rank them from 1 to 4, where 1 is the fastest and 4 is the slowest. (Let π = .)
7
_____ A wheel of radius 28 cm moving at 60 rpm = ______ m/s
_____ A plane moving at a speed of 30 kph = ______ m/s
_____ A sprinter running 100 m in 15 seconds = ______ m/s
_____ A car running 72 meters after 9 seconds = ______ m/s
Test II. Average Speed
Determine the average speed of the following object.
1. A car speed tabulated for every seconds under a 10-second time duration.
Speed 0 10 8 7 10 15 8 7 10 10 15 m/s
time 0 1 2 3 4 5 6 7 8 9 10 sec
2. A runner whose movement is as follow: 200 m for 80 sec, 100 m for 30 sec, and 300 m for 90
sec.
Test III. How fast you move.
Fill up the table below (Use approximate values) and calculate your speed in m/s for that
activity.
Activity Distance Time Consumed Average Speed
Walking (House to School) meters __hr __min __sec m/s
Climbing a Staircase meters __hr __min __sec m/s
Riding a Bicycle meters __hr __min __sec m/s
Going to the Mall meters __hr __min __sec m/s
Swimming meters __hr __min __sec m/s
Walking (Classroom to Canteen) meters __hr __min __sec m/s

6. Activity #2
Test I. Speed Vs. Velocity
Determine whether the following suggest speed or velocity. Write S for speed and V for velocity.
_____ An elevator moving for 30m from the first floor to the third floor for 5 minutes.
_____ A man walked for half an hour and covered 600 meters.
_____ A ball dropped 30 m above a building is found on the ground 3 seconds after.
_____ The news reported that the speed of Hanging Habagat is 20 km/h.
_____ A sprinter finish a 400 meter race after 2 minutes and 16 seconds.
Test II. The Friendly Race
Read and analyze the situation. Answer the questions that follow.
4 friends decided to have a race from the gate of their school to the beach. The
beach is 30 km north of the starting position. Since the friends are racing from each other they
decided to take different paths.
Ramon: 20 km North for 15 minutes; 5 km N 30° E for 5 minutes; and 5 km West for 5 minutes.
Ronald: 20 2 km NW for 27 minutes; 20 km East for 20 minutes; and 10 km North for 6
minutes.
Eduard: 15 km North for 10 minutes; 15 km West for 11 minutes; and 15 2 km NE for 15
minutes.
Adolfo: 50 km N 60° E for 50 minutes; 15 km West for 11 minutes; and 5 km South for 7
minutes.
1. Complete the table below.
Name Total Distance Total Time Average Speed
Ramon km __hr __min km/h
Ronald km __hr __min km/h
Eduard km __hr __min km/h
Adolfo km __hr __min km/h
2. Who did not finish the race?
3. Who finished the race?

7. 4. Who won the race?
5. Using the Cartesian plane below, plot the movement of each friend.
(Use the scale 1 unit: 5 km and let the starting position be at the origin.)
6. From the plot above, determine the displacement of the four friends. (Round off answers to two decimal
places)
Name Displacement
Ramon km
Ronald km
Eduard km
Adolfo km
7. Calculate the average velocity of the four friends. (Round off answers to two decimal places)
Name Average Velocity
Ramon _____ km/h ______
Ronald _____ km/h ______
Eduard _____ km/h ______
Adolfo _____ km/h ______

8. Assessment Card #2
Test I. Multiple Choice. (Use π=3.14)
1. A plane’s speed after landing is defined by the equation s = 180 − 18t m s , how long would
it take the plane to stop?
a. 10 seconds b. 11 seconds c. 12 seconds d. 13 seconds
2. A 50 m train of constant speed enters a 300 m tunnel, if a stationary light located in the
tunnel has been above the train for 4 seconds. How fast is the train moving?
a. 10 m/s b. 12.5 m/s c. 15 m/s d. 17.5 m/s
3. A car was able to take 10 laps in a circular race track whose radius is 15 m for a total time
of 15 minutes and 42 second. What is the average speed of the car?
a. 10 km/h b. 20 km/h c. 30 km/h d. 40 km/h
4. Two men were walking towards each other. The speed of the first man (A) is 2/3 of the
speed of the second man (B) and the distance between them is 150m. After t seconds the
two men meet each other, by this point how far did man A travelled?
a. 50 m b. 60 m c. 70 m d. cannot be
determined
5. A runner ran around an oval and returned to his original position. If the average speed of
the runner is 2 mph and he ran for 13 minutes, which of the following could be his
velocity?
a. 2 mph East b. 0 mph North c. 4 mph East d. 1 mph North
Test II. Matching Type – Match Column A with Column B. Connect the Circles of the
corresponding matches.
Column A Column B
1. The rate at which an object covers a distance. • • A. Odometer
2. The distance of the line connecting the initial • • B. Velocity
and the final position.
3. The rate at which an object moves with respect • • C. Displacement
to direction.
4. It refers to how fast an object is moving in • • D. Speed
a given period of time
5. A device used to measure speed. • • E. Instantaneous Speed

9. Enrichment #1
Test I. Vocabulary Enhancement
Define the following:
1. Average Speed
2. Azimuth
3. Direction
4. Displacement
5. Instantaneous Speed
6. Kinematics
7. Scalar Quantity
8. Speed
9. Vector Quantity
10. Velocity
Test II. Relationship of Distance, Time, Speed and Velocity
Match the definition with the appropriate illustration below.
a. b. c. d.
____ Constant Speed
____ Zero Displacement
____ Increasing Speed
____ Zero Velocity
____ Constant Velocity
Test II. Essay
A. Explain why it is possible to have positive average speed but zero average velocity.
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
________.
B. Explain the difference between a vector and a scalar quantity.
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
________.

10. Enrichment #2
Test I. Which Car was that?
Two cars were moving at constant speed. Car A is moving at a rate of (1)_____ mph.
Car B is moving at 80 mph. After 3 hours Car A is 27 miles from Car B which by this
time has travelled (2) _____. Two hours earlier Car A is (3) _____ miles ahead of Car B.
On the fourth hour, Car B decided to stop for (4) _____ minutes. From the moment
Car B stopped till it started to continue its track Car A has travelled (5)____ miles
making the distance between the two cars equal to 80.5 miles. (6-10) If a snail moving
at a rate of 0.0000001 mile/s crossing the road 500 miles away from the starting
point and the road is 0.004 mile wide which car is closer to the snail when it reaches
the middle of the road?(The snail started crossing the moment the two cars started
the moving.)
Test II. Average Velocity (Use 1:20meters and 1:5naut.miles in plotting)
Plot the movement of the following objects and determine their average velocity.
1. A ship move at a speed of 30 knots with a bearing of 120° for half an hour. Then
turned 30° to the left and travelled 20 n.m. for 45 minutes to reach its destination.
2. To reach the school, Ramon walked the following distance: 160m N 30° E for 3
minutes; 100m West for 5 minutes; and 20 2 m NE for 2 minutes.
y
9
8
7
6
5
4
3
2
1
x
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
-1
-2
-3
-4
-5
-6
-7
-8
-9

11. Enrichment #3 Top Ten (10) Fastest Land Animals
1. Cheetah (70 mph)
The cheetah is the fastest member of the cat family and is unique
because what it lacks in climbing abilities it makes up for in speed and stealth.
The cheetah is the fastest of all land animals and can reach speeds between
112 kilometres per hour (70 mph) and 120 kilometres per hour (75 mph) in
short bursts up to 460 metres (500 yd). The cheetah's ability to accelerate is
unmatched. The animal can easily accelerate from 0 to 110 kilometres per
hour (68 mph) in three seconds, faster than most supercars.
2. Pronghorn Antelope (61 mph)
The Pronghorn Antelope's exceptional speed is necessary in order to
evade predators by outrunning them. The animal is considered to be the fastest
animal in the new world. The top speed is very hard to measure accurately and it
varies between individuals, however the animal has been clocked at 61mph. It is
often cited as the second-fastest land animal with the Cheetah being the fastest.
The animal can sustain these speeds much longer than a cheetah due to its
larger heart and lungs. These animals are poor jumpers.
3. Wildebeest (50 mph)
The Wildebeest is another animal that relies on its speed to evade
predators. These animals are favorites of the big cats as they inhabit the plains
and open woodlands of Africa. They are most plentiful in the Serengeti and
can live more than 20 years.
4. Lion (50 mph)
The king of bests doesn't often use his speed when hunting because
the lioness does the majority of the hunting. Those Lions without a pride use
clever stealth and speed to catch their prey. Males can exceed 550lbs, making
it the second largest living cat after the tiger. Wild lions can only be found in
sub-Saharan Africa, Asia and a small population in northwest India.
5. Thomson’s Gazelle (50 mph)
Named after explorer Joseph Thompson, the Thompson's Gazelle is
one of the best known gazelles. In order to evade its main enemy, the
cheetah, these animals can reach speeds of 50 mph, and can sustain longer
bursts than their mortal enemy.
6. Quarterhorse (47.5 mph) 8. Cape Hunting Dog (45 mph) 10. Gray Fox (42 mph)
7. Elk (45 mph) 9. Coyote (43 mph)

12. Assessment #1
UP-SIDE-DOWN WORD SEARCH
Direction
Instruction: Connect the letters inside the box to form the word that answers the question
or completes the statement. You may connect adjacent letters upward, downward and
sideward. You are not allowed to connect letters diagonally. Find the 8 Items to uncover the
mystery word using the unused letters.
K S C A L A I E Example
D I T O R R A G N B I T
P S C E O E R N O M R E
L A C V U N A E C P E S
M A E M S A V A I U T A
N A L E N T T I
I T S T A N I A
F I N I C I S L
1. _______ is an entity characterized by a magnitude and a direction.
2. Average speed is the mean of all the ___________ speed recorded for a certain period of
time.
3. The length of the line directly connecting the initial and the final position.
4. Speed is not direction aware making it a _______ quantity.
5. The ratio of the displacement and the total time is called ________ velocity.
6-7. An object has zero displacement if its _______ and ________ positions is the same.
8. What is the displacement if an object moved 6 km East and 8 km North?
9. The mystery word is __________.
10. Give your own definition of the mystery word: __________________________________
_____________________________________________________________________
____________________________________________________________________.

13. Activity #1
Test I. Ranking Speed
Given are four objects with varying speed. Convert the speed of each object to the desired unit
22
and rank them from 1 to 4, where 1 is the fastest and 4 is the slowest. (Let π = .)
7
See next page
4 A wheel of radius 28 cm moving at 60 rpm = 1.76 m/s
for the solution.
1 A plane moving at a speed of 30 kph = 8.33 m/s
3 A sprinter running 100 m in 15 seconds = 6.67 m/s
2 A car running 72 meters after 9 seconds = 8.00 m/s
Test II. Average Speed
Determine the average speed of the following objects.
1. A car speed tabulated for every seconds under a 10-second time duration.
Speed 0 10 8 7 10 15 8 7 10 10 15 m/s
save = 10 m / s
time 0 1 2 3 4 5 6 7 8 9 10 sec
2. A runner whose movement is as follow: 200 m for 80 sec, 100 m for 25 sec, and 300 m for 90
sec.
s ave = 3 m / s
Test III. How fast you move.
Fill up the table below (Use approximate values) and calculate your speed in m/s for that
activity.
Activity Distance Time Consumed Average Speed
Answers for this activity may __hr __minSee to it that the
Walking (House to School) meters vary. __sec m/s
Climbing a Staircase meters __hr __min __sec m/s
Average Bicycle
Riding a speed calculated is correct as what is
meters __hr __min __sec m/s
recorded in the distancemeters the time consumed.
Going to the Mall
Swimming
and __hr __min __sec
meters __hr __min __sec
m/s
m/s
Walking (Classroom to Canteen) meters __hr __min __sec m/s

14. Solutions for Activity I Test I
8.00 m/s
Solutions for Activity I Test II
1. A car speed tabulated for every seconds under a 10-second time duration.
Speed 0 10 8 7 10 15 8 7 10 10 15 m/s
time 0 1 2 3 4 5 6 7 8 9 10 sec
To determine the average speed, we will calculate the mean of instantaneous speed of the
car as recorded in the table.
10
∑s 10 + 8 + 7 + 10 + 15 + 8 + 7 + 10 + 10 + 15 100
s ave = n =1
s ave = s ave = s ave = 10 m / s
n 10 10
2. A runner whose movement is as follow: 200 m for 80 sec, 100 m for 30 sec, and 300
m for 90 sec.
s ave =
∑d s ave =
200 + 100 + 300
s ave =
600
s ave =
600
s ave = 3 m / s
∑t 80 + 30 + 90 200 200

15. Activity #2
Test I. Speed Vs. Velocity
Determine whether the following suggest speed or velocity. Write S for speed and V for velocity.
V An elevator moving 30m from the first floor to the third floor for 5 minutes (Upward)
S A man walked for half an hour and covered 600 meters.
V A ball dropped 30 m above a building is found on the ground 3 seconds after. (Downward)
V The news reported that the speed of Hanging Habagat is 20 km/h. (Southwest)
S A sprinter finishes a 400 meter race after 2 minutes and 16 seconds.
Test II. The Friendly Race
Read and analyze the situation. Answer the questions that follow.
4 friends decided to have a race from the gate of their school to the beach. The beach is
30 km north of the starting position. Since the friends are racing from each other they decided
to take different paths.
Ramon: 20 km North for 15 minutes; 5 km N 30° E for 5 minutes; and 5 km West for 5 minutes.
Ronald: 20 2 km NW for 27 minutes; 20 km East for 20 minutes; and 10 km North for 6
minutes.
Eduard: 15 km North for 10 minutes; 15 km West for 11 minutes; and 15 2 km NE for 15
minutes.
Adolfo: 50 km N 60° E for 50 minutes; 15 km West for 11 minutes; and 5 km South for 7
minutes.
1. Complete the table below.
Name Total Distance Total Time Average Speed
Ramon 30 km 0 hr 25 min 72.00 km/h
Ronald 58 km 0 hr 53 min 65.66 km/h
Eduard 51 km 0 hr 36 min 85.00 km/h
Adolfo 70 km 1 hr 08 min 61.76 km/h
2. Who did not finish the race?
Ramon and Adolfo
3. Who finished the race?
Ronald and Eduard

16. 4. Who won the race? Eduard won the race for reaching the beach with a total time of 36
minutes.
5. Using the Cartesian plane below, plot the movement of each friend.
(Use the scale 1 unit: 5 km and let the starting position be at the origin.)
6. From the plot above, determine the displacement of the four friends. (Round off answers to two decimal
places.)
Name Displacement
Ramon 24.46 km
Ronald 30.00 km
Eduard 30.00 km
Adolfo 34.65 km
7. Calculate the average velocity of the four friends. (Round off answers to two decimal places.)
Name Average Velocity See next page
Ramon 58.70 km/h N 5.87° W for the solution.
Ronald 33.96 km/h North
Eduard 50.00 km/h North
Adolfo 30.57 km/h N 54.75° E

17. Solutions for items number 6 and 7.
6. To calculate for displacement, we use component method.
Ramon: 20 km North for 15 min; 5 km Displacement Direction X-component Y-component
N 30° E for 5 min; and 5 km West for 20 km North 0 20
5 min. 5 km N 30° E 2.5
2.5 3
5 km W -5 0
Total -2.5
20+2.5 3
(∑ x − component ) + (∑ y − component ) (− 2.5)2 + (20 + 2.5 )
2 2 2
D= D= 3 D ≈ 24.46 km
Ronald: 20 2 km NW for 27 min; Displacement Direction X-component Y-component
20 km East for 20 min; and 10 km 20 2 km NW -20 20
North for 6 minutes. 20 km E 20 0
10 km N 0 10
Total 0 30
D= (∑ x − component ) + (∑ y − component )
2 2
D= (0)2 + (30)2 D = 30.00 km
Eduard: 15 km North for 10 min; 15 Displacement Direction X-component Y-component
km West for 11 min; and 15 2 km 15 km N 0 15
15 km W -15 0
NE for 15 min.
15 2 km NE 15 15
Total 0 30
D= (∑ x − component ) + (∑ y − component )
2 2
D= (0)2 + (30)2 D = 30.00 km
Adolfo: 50 km N 60° E for 50 min; Displacement Direction X-component Y-component
50 km N 60° E 25
15 km West for 11 min; and 5 km 25 3
South for 7 min. 15 km W -15 0
5 km S 0 -5
Total 20
25 3 -15
D= (∑ x − component ) + (∑ y − component )
2 2
D= (25 )
3 − 15 + (20 )
2 2
D ≈ 34.65 km
7. For the direction of the velocity use the results of the component method in item number 6.
y 20 + 2.5 3
Ramon: tan
−
θ= tan − θ = tan − θ = −9.732050808 θ = −84.13
x − 2.5
24.46
Therefore, Ramon’s average velocity is N 90 − 84.13°W = 58.70 N 5.87°W
25 min
y 30 30
Ronald: tan
−
θ= tan − θ = tan − θ = undefined θ = 90° Therefore, Ronald’s vave= =
x 0 53 min
33.96km / h N
y 30 30
Eduard: tan
−
θ= tan − θ = tan − θ = undefined θ = 90° Therefore, Eduard’s vave= =
x 0 36 min
50.00km / h N
y 20
Adolfo: tan
−
θ= tan − θ = tan − θ = 0.070668 θ = 35.25
x 25 3 − 15
34.65
Therefore, Adolfo’s average velocity is N 90 − 35.25° E = 30.57 km / h N 54.75° E
68 min

18. Assessment #1
UP-SIDE-DOWN WORD SEARCH
Direction
Instruction: Connect the letters inside the box to form the word that answers the question
or completes the statement. You may connect adjacent letters upward, downward and
sideward. You are not allowed to connect letters diagonally. Find the 8 Items to uncover the
mystery word using the unused letters.
1. VECTOR is an entity characterized by a magnitude and a direction.
2. Average speed is the mean of all the INSTANTENOUS speed recorded for a certain period
of time.
3. The length of the line directly connecting the initial and the final position. DISPLACEMENT
4. Speed is not direction aware making it a SCALAR quantity.
5. The ratio of the displacement and the total time is called AVERAGE velocity.
6-7. An object has zero displacement if it’s INITIAL and FINAL positions is the same.
8. What is the displacement if an object moved 6 km East and 8 km North? TEN (10 km)
9. The mystery word is KINEMATICS.
10. Give your own definition of the mystery word:
Kinematics is the study of motion and its components.

19. See next page for
Assessment Card #2 the solution.
Test I. Multiple Choice. (Use π=3.14)
1. A plane’s speed after landing is defined by the equation s = 180 − 18t m s , how long would
it take the plane to stop?
a. 10 seconds b. 11 seconds c. 12 seconds d. 13 seconds
2. A 50 m train of constant speed enters a 300 m tunnel, if a stationary light located in the
tunnel has been above the train for 4 seconds. How fast is the train moving?
a. 10 m/s b. 12.5 m/s c. 15 m/s d. 17.5 m/s
3. A car was able to take 10 laps in a circular race track whose radius is 15 m for a total time
of 15 minutes and 42 second. What is the average speed of the car?
a. 10 km/h b. 20 km/h c. 30 km/h d. 40 km/h
4. Two men were walking towards each other. The speed of the first man (A) is 2/3 of the
speed of the second man (B) and the distance between them is 150m. After t seconds the
two men meet each other, by this point how far did man A travelled?
a. 50 m b. 60 m c. 70 m d. cannot be
determined
5. A runner ran around an oval and returned to his original position. If the average speed of
the runner is 2 mph and he ran for 13 minutes, which of the following could be his
velocity?
a. 2 mph East b. 0 mph North c. 4 mph East d. 1 mph North
Test II. Matching Type – Match Column A with Column B. Connect the Circles of the
corresponding matches.

20. Solutions for Assessment Card #2 Test 1

21. Enrichment #1
Test I. Vocabulary Enhancement
Define the following:
1. Average Speed is the ratio of the total distance travelled to the total time.
2. Azimuth is a horizontal angle measured clockwise from a north base line or meridian.
3. Direction is the line or course upon which anything is moving or aimed to
move, or in which anything is lying or pointing.
4. Displacement is the length of the track connecting the initial and the final
position.
5. Instantaneous Speed is the speed of an object at a given moment of time.
6. Kinematics is the study of motion and its components.
7. Scalar Quantity is a simple physical quantity that is not direction aware.
8. Speed the rate at which an object is moving.
9. Vector Quantity a quantity having a magnitude and a direction.
10. Velocity the speed at which an object is moving with respect to the direction.
Test II. Relationship of Distance, Time, Speed and Velocity
Match the definition with the appropriate illustration below.
a. b. c. d.
a & c Constant Speed
b Zero Displacement
d Increasing Speed
b Zero Velocity
a & c Constant Velocity
Test II. Essay
A. Explain why it is possible to have positive average speed but zero average velocity.
It is possible to have zero average velocity but a positive average speed since average
speed only takes the total distance covered over the total time while average velocity
takes the displacement over the total time. Assuming that the initial and the final
position is the same, the displacement would be equal to zero thus yielding zero average
velocity.
B. Explain the difference between a vector and a scalar quantity.
A vector quantity contains a magnitude and a direction while a scalar quantity has only the
magnitude.

22. Enrichment #2
Test I. Which Car was that?
Two cars were moving at constant speed. Car A is moving at a rate of (1) 89 mph. Car
B is moving at 80 mph. After 3 hours Car A is 27 miles from Car B which by this time
has travelled (2) 240 miles. Two hours earlier Car A is (3) 9 miles ahead of Car B. On the
fourth hour, Car B decided to stop for (4) 30 minutes. From the moment Car B
stopped till it started to continue its track Car A has travelled (5) 44.5 miles making
the distance between the two cars equal to 80.5 miles. (6-10) If a snail moving at a rate
of 0.0000001 mile/s crossing the road 500 miles away from the starting point and the
road is 0.004 mile wide which car is closer to the snail when it reaches the middle of
the road?(The snail started crossing the moment the two cars started the moving.)
Car A is closer to the snail. (See next page for the solutions.)
Test II. Average Velocity (Use 1:20meters and 1:5naut.miles in plotting)
Plot the movement of the following objects and determine their average velocity.
1. A ship move at a speed of 30 knots with a bearing of 120° for half an hour. Then
turned 30° to the left and travelled 20 n.m. for 45 minutes to reach its destination.
27.06 knots E 12.81° S
2. To reach the school, Ramon walked the following distance: 160m N 30° E for 3
minutes; 100m West for 5 minutes; and 20 2 m NE for 2 minutes.
1. Ship y
9
1. Ship's Average Velocity
2. Ramon 8
2. Ramon's Average Velocity 7
6
5
4
3
2
1
x
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
-1
-2
-3
-4
-5
-6
-7
-8
-9

23. Solutions for Enrichment #2
Test I.
1. It is given that both moved at a constant speed. By examining and using the clue in sentence
number four that states that car A is ahead of Car B. we can conclude that car A’s speed is 89 mph.
Using this we can therefore solve the rest of the items.
miles
2. 80 × 3h = 240 miles
h
3. Given t=1, Sa = 89 mph and Sb = 80 mph. d a − d b = (89 − 80 )1 = 9miles
4. Using the answer on the next item we will be able to know how long did car b stopped.
d 44.5mi
t= = = 0.5h = 30 min
s mi
90
h
5. We difference of the two cars on the fourth hour.
t=4, Sa = 89 mph and Sb = 80 mph. d a − d b = (89 − 80 )4 = 36miles
Subtract the value to the total distance on the moment car B Decided to continue.
80.5 − 36 = 44.5miles
6-10. We first Calculate the time it took the snail to reach the middle.
0.004 ÷ 2(half the length of the road ) 0.002mi s
t= = × = 20000 sec = 5 hr 20 min 33 sec
m 1 0.0000001mi
0.0000001
s
Determine the distance cover by the two cars.
3. Given t=1, Sa = 89 mph and Sb = 80 mph.
t 20000 sec 20000 sec 89mi 1h
da = = = x × = 494.44 miles
sa mi 1 h 3600 sec
89
h
t 20000 sec− (.5 × 3600) 18200 sec 80mi 1h
da = = = x × = 404.44 miles
sa mi 1 h 3600 sec
80
h
We subtracted half an hour since car b is not moving for that period of time from the 4th hour to the
4.5th hour. With distance travelled above by the two cars. We can conclude that car A is closer to the
snail which is found on the 500th mile of the track.
Test II. Use component method to know the average velocity.
1. A ship move at a speed of 30 Displacement Direction X-component Y-component
knots with a bearing of 120° for half 15n.m. 120° bearing 7.5 3 -7.5
an hour. Then turned 30° to the left 20n.m East 20 0
and travelled 20 n.m. for 45
Total 20 + 7.5 3 -7.5
minutes to reach its destination.
D= (∑ x − component ) + (∑ y − component )
2 2
D= (20 + 7.5 3 ) 2
+ (− 7.5)
2
D ≈ 33.83 nm
( (
Vave = 33.83 ÷ (.5 + .75) arctan − 7.5 ÷ 20 + 7.5 3 )) Vave = 27.06 knots E 12.81°S
Displacement Direction X-component Y-component
2. To reach the school, Ramon
160 m N 30° E 80 80 3
walked the following distance: 160m
100 m W -100 0
N 30° E for 3 minutes; 100m West
20 2 m NE 20 20
for 5 minutes; and 20 2 m NE for 2
Total 0 20 + 80 3
minutes.
(∑ x − component ) + (∑ y − component ) (0)2 + (20 + 80 )
2 2 2
D= D= 3 D = 158.56 m
m
Vave = 158.56m ÷ (10 min) North Vave = 15.86 North
min

24. BOOKS
• Richard P. Feynman, Robert B. Leighton, Matthew
Sands. The Feynman Lectures on Physics, Volume I,
Section 8-2. Addison-Wesley, Reading, Massachusetts
(1963). ISBN 0-201-02116-1.
• Robert Resnick and Jearl Walker, Fundamentals of
Physics, Wiley; 7 Sub edition (June 16, 2004). ISBN
0471232319.
INTERNET
• http://www.physicslab.com/speed&velocity.html
• http://www.petsdo.com/blog/top-twenty-20-fastest-
land-animals-including-humans
• http://en.wikipedia.org/wiki/Speed
• http://en.wikipedia.org/wiki/Velocity