Speed and Velocity

Re R e p u b l i c o f t h e P h i l i p p i n e s D e p a r t m e n t o f E d u c a t i o n R e g i o n V I I , C e n t r a l V i s a y a s D i v i s i o n o f M a n d a u e C i t y

Labogon, Mandaue City

SPEED AND VELOCITY

Prepared by: RHONNEL M. ALBURO IV - Galatia

Visit my website: http://www.alfore.info/ http://www.alfore.info/ to to see my collection collection of school related works!

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 VIII. Assessment Card #2 IX.

Enrichment Card #1

X.

Enrichment Card #2

XI.

Enrichment Card #3

XII. Answer Card XIII. Reference XIII. Reference Card

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.

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!

Activity #1 Test I. Ranking Speed Given are four objects with varying speed. Convert the speed of each object to the t he desired unit and rank them from 1 to 4, where 1 is the fastest and 4 is the s lowest. (Letπ = _____ A wheel of radius 28 cm moving moving at 60 rpm _____ A plane moving at a speed of 30 kph _____ A sprinter running 100 m in 15 seconds _____ A car running 72 meters meters after 9 seconds

22 7

.)

= ______ ______ m/s = ______ ______ m/s = ______ ______ m/s = ______ ______ m/s

Test II. Average Speed Determine the average speed of the following f ollowing object. 1. A car speed tabulated for every e very seconds under a 10-second time duration. Speed time

0 0

10 1

8 2

7 3

10 4

15 5

8 6

7 7

10 8

10 9

15 10

m/s 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. m ove. Fill up the table below (Use approximate values) and calculate your speed in m/s for that activity. Activity Walking (House to School) Climbing a Staircase Riding a Bicycle Going to the Mall Swimming Walking (Classroom to Canteen)

Distance Distance meters meters meters meters meters meters

Time Consumed __hr __min __min __sec __hr __min __min __sec __hr __min __min __sec __hr __min __min __sec __hr __min __min __sec __hr __min __min __sec

Average Speed m/s m/s m/s m/s m/s m/s

Activity #2 Test I. Speed Vs. Velocity Determine whether the following suggest speed or velocity. Write S for speed and V for velocity. _____ An An elevator moving for 30m from the first floor to the third third floor for 5 minutes. _____ A man walked for half an an hour and covered 600 meters. meters. _____ A ball dropped 30 m above above a building is found on the ground ground 3 seconds after. _____ The The news reported that the speed of of Hanging Habagat is 20 km/h. _____ A sprinter finish a 400 meter 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 d ifferent paths. Ramon: 20 km North for 15 minutes; 5 km N 30° E for 5 minutes; and 5 km West for 5 minut es. 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; minutes; 15 km West for 11 minutes; and 5 km South for 7 minutes. 1. Complete the table below. Name Ramon Ronald Eduard Adolfo 2. Who did not finish f inish the race?

3. Who finished the race?

Total Distance km km km km

Total Time __hr __min __min __hr __min __min __hr __min __min __hr __min __min

Average Speed km/h km/h km/h km/h

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 displ acement of the four friends. (Round off answers to two decimal places)

Name Ramon Ronald Eduard Adolfo

Displacement km km km km

7. Calculate the average velocity of the four friends. (Round off answers to two decimal places)


Average Velocity _____ km/h ______ _____ km/h ______ _____ km/h ______ _____ km/h ______

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 s tationary 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 t ime of 15 minutes and 42 second. What is the average speed of the t he car? a. 10 km/h b. 20 km/h c. 30 km/h d. 40 km/h 4. Two men were walking towards each 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 f ar 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 1. The rate at which an object o bject covers a distance. 2. The distance of the line connecting the initial and the final position. 3. The rate at which an object moves with respect to direction. 4. It refers to how fast an object is moving in a given period of time 5. A device used to measure speed.

Column B •

•

•

•

A. Odometer B. Velocity

•

•

C. Displacement Displacement

•

•

D. Speed

•

•

E. Instantaneous Speed

Enrichment #1 Test I. Vocabulary Enhancement Define the following: 1. Average Speed 2. Azimuth 3. Direction 4. Displacement 5. Instantaneous 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 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. _________________________ ____________________________________ _____________________ ______________________ _________________________ ________________________ ___________ _________________________ ____________________________________ _____________________ ______________________ _________________________ ________________________ ___________ _________________________ ____________________________________ _____________________ ______________________ _________________________ ________________________ ___________ ________.

Enrichment #2 Test I. Which Car was that? (1)

Two cars were moving at constant speed. Car A is moving at a rate of _____ mph. Car B is moving at 80 mph. After 3 hours Car A is 27 miles from Car B which by this (2) (3) time has travelled _____. Two hours earlier Car A is _____ miles miles ahead of Car B. (4) On the fourth hour, Car B decided to stop for _____ minutes. From the moment (5) Car B stopped till it started to continue its track Car A has travelled ____ miles (6-10) making the distance between the two cars equal to 80.5 miles. 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 -8

-7

-6

-5 -5

-4

-3

-2

-1 -1

1 -1 -2 -3 -4 -5 -6 -7 -8 -9

2

3

4

5

6

7

8

9

Enrichment #3

Top Ten (10) Fastest Land Animals 1. Cheetah (70 mph) The cheetah is the fastest member of the cat family and is u nique because what it lacks in climbing abilities it makes up for in speed and st ealth. 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. worl d. 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 e vade 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 Serenget i 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 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)

7. Elk (45 mph)

8. Cape Hunting Dog (45 mph)

9. Coyote (43 mph)

10. Gray Fox (42 mph)

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 D P L M N I F

S I S A A A T I

C T C C E L S N

A O E V M E T I

L R O U S N A C

A R E N A T N I

I A R A V T I S

E G N E A I A L

Example Example N B O M C P I U

I R E T

T E S A

1. _______ is an entity characterized by a magnitude and a direction. 2. Average speed is the mean of all the ___________ speed recorded recorded for a certain period of time. 3. The length of the line directly connecting the initial and the f inal position. 4. Speed is not n ot direction aware making it a _______ quantity. 5. The ratio of the displacement and the total time is called ________ velocity. 6-7. An object has zer o 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 w ord is __________. 10. Give your own definition def inition of the mystery word: __________________ ___________________________ ________________ _______ _________________ _________________________ _________________ _________________ __________________ __________________ _______________ _________ __ _________________ _________________________ _________________ _________________ __________________ __________________ _______________ ________. _.

Activity #1 Test I. Ranking Speed Given are four objects with varying speed. Convert the speed of each object to the t he desired unit and rank them from 1 to 4, where 1 is the fastest and 4 is the s lowest. (Letπ = 4 1 3 2

A wheel of radius 28 cm moving at 60 rpm A plane moving at a speed of 30 kph A sprinter running 100 m in 15 seconds A car running 72 meters after 9 seconds

= = = =

1.76 8.33 6.67 8.00

22 7

.)

See next page

m/s m/s m/s m/s

for the solution.

Test II. Average Speed Determine the average speed of the following f ollowing objects. 1. A car speed tabulated for every seconds under a 10-second time duration. Speed time

0 0

10 1

8 2

7 3

10 4

15 5

8 6

7 7

10 8

10 9

15 10

m/s sec

save = 10 m / s

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. m ove. Fill up the table below (Use approximate values) and calculate your speed in m/s f or that activity. Activity Walking (House to School) Climbing a Staircase Riding a Bicycle Going to the Mall Swimming Walking (Classroom to Canteen)

Distance Distance meters meters meters meters meters meters

Time Consumed

Average Speed m/s m/s m/s m/s m/s m/s

Answers for this activity may __hr vary. __min __minSee __sec to it that the __hr __min __min __sec

Average speed calculated is __hrcorrect __min __min __sec as what is __hr __min __min __sec

recorded in the distance and the time consumed. __hr __min __min __sec __hr __min __min __sec

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 time

0 0

10 1

8 2

7 3

10 4

15 5

8 6

7 7

10 8

10 9

15 10

m/s sec

To determine the average speed, we will calculate the mean of instantaneous speed of the car as recorded in the table. 10

∑s s ave =

n =1

s ave =

n

10 + 8 + 7 + 10 + 15 + 8 + 7 + 10 + 10 + 15 10

s ave =

100 10

s ave = 10 m / s

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 ∑ t

s ave =

200 + 100 + 300 80 + 30 + 90

s ave =

600 200

s ave =

600 200

s ave = 3 m / s

Activity #2 Test I. Speed Vs. Velocity Determine whether the following suggest speed or velocity. Write S for speed and V for velocity. V S V V S

An elevator moving 30m from the first floor f loor to the third floor for 5 minutes (Upward ) 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. (Downward ) The news reported that the speed of Hanging Habagat is 20 km/h. (Southwest ) 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; m inutes; 15 km West for 11 1 1 minutes; and 15 2 km NE for 15 minutes. Adolfo: 50 km N 60° E for 50 minutes; minutes; 15 km West for 11 minutes; and and 5 km South for 7 minutes. 1. Complete the table below. Name Ramon Ronald Eduard Adolfo 2. Who did not finish f inish the race? Ramon and Adolfo 3. Who finished the race? Ronald and Eduard

Total Distance 30 km 58 km 51 km 70 km

Total Time 0 hr 25 min 0 hr 53 min 0 hr 36 min 1 hr 08 min

Average Speed 72.00 km/h 65.66 km/h 85.00 km/h 61.76 km/h

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 displ acement of the four friends. (Round off answers to two decimal places.)


Displacement 24.46 km 30.00 km 30.00 km 34.65 km

7. Calculate the average velocity of the four friends. (Round off answers to two decimal places.)


Average Velocity 58.70 km/h N 5.87° W 33.96 km/h North 50.00 km/h North 30.57 km/h N 54.75° E

See

next

page

for the solution.

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 Displaceme nt N 30° E for 5 min; and 5 km West for 20 km 5 min. 5 km

Direction North N 30° E

X-component X-componen t 0 2.5

Y-component Y-componen t 20

W

-5 -2.5

0

5 km Total

D =

(∑ x − component ) + (∑ y − component ) 2

2

Ronald: 20 2 km NW for 27 min;

Displacement Displaceme nt

20 km East for 20 min; and 10 km North for 6 minutes.

20 2 km 20 km 10 km

(− 2.5)2 + (20 + 2.5

D =


2

Eduard: 15 km North for 10 min; 15 km West for 11 min; and 15 2 km NE for 15 min.

15


2

Adolfo: 50 km N 60° E for 50 min; 15 km West for 11 min; and 5 km

0 10 30

(0)2 + (30) 2

D =

D = 30.00 km

X-component X-componen t 0 -15 15

Y-component Y-componen t 15 0 15

0

30

(0)2 + (30) 2

Direction N 60° E

15 km 5 km

W S


2

D =

25

3


-15 0 25

(25

D = 30.00 km

X-component X-compone nt

Total

D =

D ≈ 24.46 km

20 0 0

Displacement Displaceme nt 50 km

South for 7 min.

2

E N

Total

D =

)


Direction N W NE

2 km

3

3 − 15

)

2

0 -5 20

3 -15

+ (20)

2

D ≈ 34.65 km

7. For the direction of the velocity use the results of the component method in item number 6. −

Ramon: tan θ =

y x

tan

−

θ =

20 + 2.5 3

Therefore, Ramon’s average velocity is −

Ronald: tan θ =

y x

tan

−

tan

−

θ =

tan − θ = −9.732050808 θ = −84.13

− 2.5

30

24.46 25 min

N 90 − 84.13°W = 58.70 N 5.87°W

−

tan θ = undefined

0

θ =

90° Therefore, Ronald’s v ave=

θ =

90° Therefore, Eduard’s vave=

30 53 min

=

33.96km / h N −

Eduard: tan θ =

y x

θ =

30

−

tan θ = undefined

0

50.00km / h N −

Adolfo: tan θ =

y x

−

tan θ =

20 25 3 − 15 34.65

Therefore, Adolfo’s average velocity is

68 min

3

X-component X-componen t -20

D =

Displacement Displaceme nt 15 km 15 km

20+2.5

Direction NW

Total

D =

3

2.5

tan − θ = 0.070668 θ = 35.25 N 90 − 35.25°E = 30.57 km / h N 54.75° E

30 36 min

=

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 f inal 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 mys tery word:

Kinematics is the study of motion and its components. compo nents.

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? b. 12.5 m/s a. 10 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 t ime of 15 minutes and 42 second. What is the average speed of the t he car? a. 10 km/h b. 20 km/h c. 30 km/h d. 40 km/h 4. Two men were walking towards each 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 f ar 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? b. 0 mph North a. 2 mph East 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.

Solutions for Assessment Card #2 Test 1

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 an gle 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 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 scal ar quantity.

A vector quantity contains a magnitude and a direction while a scalar quantity has only the magnitude.

Enrichment #2 Test I. Which Car was that? (1)

Two cars were moving at constant speed. Car A is moving at a rate of 89 mph. Car B is moving at 80 mph. After 3 hours Car A is 27 miles from Car B which by this time (2) (3) miles. Two hours earlier Car A is 9 miles ahead of Car B. On the has travelled 240 miles. (4) 30 minutes. From the moment Car B fourth hour, Car B decided to stop for (5) 44.5 miles making stopped till it started to continue its track Car A has travelled (6-10) the distance between the two cars equal to 80.5 miles. 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. y

1. Ship 9

1. Shi S hip' p'ss Average Average Veloc Velocity ity 2. Ramon

8

2. Ramon's R amon's Average Average Velocity Velocity

7 6 5 4 3 2 1

x -9

-8

-7

-6

-5

-4

-3

-2

-1

1 -1 -2 -3 -4 -5 -6 -7 -8 -9

2

3

4

5

6

7

8

9

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, S a = 89 mph and S b = 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.

t =

d s

=

44.5mi = 0.5h = 30 min mi 90 h

5. We difference of the two cars on the fourth hour. t=4, Sa = 89 mph and S b = 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

0.0000001

m

1

0.0000001mi

s

Determine the distance cover by the two cars. 3. Given t=1, S a = 89 mph and S b = 80 mph.

20000 sec 20000 sec 89mi 1h x = × = 494.44 miles mi sa 1 h 3600 sec 89 h t 20000 sec− (.5 × 3600) 18200 sec 80mi 1h d a = x = = × = 404.44 miles mi sa h 1 3600 sec 80 h

d a =

t

=

th

We subtracted half an hour since car b is not moving for that period of time from the 4 hour to the th 4.5 hour. With distance travelled above by the two cars. We can conclude that car A is closer to the th snail which is found on the 500 mile of the track. Test II. Use component method to know the average velocity. 1. A ship move at a speed of 30 Displacement Displaceme nt Direction knots with a bearing of 120° for half 15n.m. 120° bearing an hour. Then turned 30° to the left 20n.m East and travelled 20 n.m. for 45 Total minutes to reach its destination.

D =


2

V ave = 33.83 ÷ (.5 + .75) arctan − 7.5 ÷ 20 + 7.5 3 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.

D =

V ave = 158.56m ÷ (10 min) North

20 20 + 7.5

(20 + 7.5 3 )

2

3

+ (− 7.5)

2

Y-component Y-componen t -7.5 0 -7.5

D ≈ 33.83 nm

V ave = 27.06 knots E 12.81° S

Displacement Displaceme nt 160 m

Direction N 30° E

X-component X-componen t 80

Y-component Y-componen t 80 3

100 m 20 2 m

W NE

-100 20 0

0 20

Total


D =

X-component X-componen t 7.5 3

2

D =

V ave = 15.86

(0 )2 + (20 + 80 m

min

North

3

)

2

20 + 80 3

D = 158.56 m

•

Richard P. Feynman, Robert B. Leighton, Matthew Sands. The Feynman Lectures on Physics, Volume I, Section 8-2. Addison-Wesley, Addison-Wesley, Reading, Massachusetts (1963). ISBN 0-201-02116-1. 0-201-02116-1.

•

Robert Resnick and Jearl Walker, Fundamentals o Physics , Wiley; 7 Sub edition (June 16, 2004). ISBN 0471232319.

•

http://www.physicslab.com/speed&velocity.html

•

http://www.petsdo.com/blog/top-twenty-20-fastestland-animals-including-humans

•

http://en.wikipedia.org/wiki/Speed

•

http://en.wikipedia.org/wiki/Velocity

Speed and Velocity

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