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GRAPHICAL REPRESENTATION OF MOTION

EVE D I S T A N C E

MAVIC

IDA

ROSE

TIME

The graph shows four beautiful runners. Basing from the graph, who is the winner? Why? Why do they have different shapes of graphline?

The possible graphs that could represent motion of a body are: 1. _________________________ d

t

2. __________________________ v t

d

Example: d(m) t(s) 50 10 100 20 150 30

200

150

2

100 1 50 t

0 0

Slope1 = y2-y1 x2-x1 Slope2 = y2-y1 x2-x1

10

20

30

=_______________________

=______________________

40

50

What did you notice about the computed slopes whose units are in m/s? _____________________ Since the speeds are the same, what kind of motion is shown in the straight-line d-t graph? __________________________

So, if the distance-time (d-t) graph is:

1. ____________________

2. ________________

3.

__________________

4.

__________________

5.

______________________

6. _______________________

7.

__________________________

8. ________________

9.

10.

________________________

________________________

From the different shapes of a d-t graph, a combination maybe possible to depict various changes in motion F

d D B

E C

G

0

A

H

t

Isaac Newton, 1642-1727 In 1666, our old friend, Isaac Newton, was musing on the motions of heavenly bodies while sitting in a garden in Lincolnshire England, where he had gone to escape the plague then ravaging London.

What if the force of gravity, the same force that causes an apple to fall to the ground in this garden, extends much further than usually thought? What if the force of gravity extends all the way to the moon? Newton began to calculate the consequences of his assumption…

17-12

Interpret the different points in the graph: 0-A

→___________________________

A-B

→___________________________

B-C

→___________________________

C-D

→___________________________

D-E

→___________________________

E-F

→___________________________

F-G →___________________________ Can you create a story out of the various graph lines?

Example:

MY WAY TO SCHOOL

I traveled with uniform speed (0-A) going to Nagtahan until I approached a stop light before the bridge so I stopped (A-B). Upon climbing the bridge I stepped on the gas pedal and the car accelerated (B-C). But a heavy traffic is building up in Lacson St. so I stopped (C-D). Finally I approached the high school building so I decreased the speed (D-E) but noticed that I left my bag, so, I drove back uniformly to Dapitan gate (E-F). Then I saw my son holding my bag along the street so I stopped (F-G) and got my bag.

Can you make your own story out of the various graphlines of a d-t graph? Were you in this situation before? You’re walking from your house in Lacson St. to the high school building. Upon reaching your classroom you noticed that the calculator you borrowed from your classmate was left at home and only your calculator is inside your bag. Your classmate is going to use it at 7am for your physics exam. No calculator, no exam! You decided to go back to your house since there is still enough time. Upon coming back you encountered an old woman who fainted near you. No other person in the vicinity

m1 m 2 F G 2 rˆ r The meaning of each term:

F: G: m1 : m2 : r2: rˆ :

Gravitational force on object 1 from object 2. –11 2 2 Universal gravitational constant = 6.673 x 10 N m /kg . Mass of object 1. Mass of object 2. Center distance from object 1 to object 2, squared. Unit vector from object 1 to object 2.

17-16

except you and the old woman. If you leave the old woman your classmate can take the test. If you assist her your classmate will get zero. What will you do and why? Are you accountable to any of them? ACTIVITY Choose your partner and sit together in one place. Get a graphing paper and write your names on it. Make a d-t graph showing at least 5 different graphlines and describe each. Write a story line out of the graphlines chosen.

ACTIVITY Choose a partner and sit together in one place. Prepare a graphing paper as your answer sheet Answer the questions in the activity sheet d D

25 20

E

15 C 10 5

A

B

F t

0

2

4

6

8

10

11

12

13

14

1. Is speed constant during any time interval? Explain. 2. At what time is the speed greatest? 3. At what time interval does the car go backward? Explain. 4. At which of the labeled points on the graph is the magnitude of the speed greatest? Explain. 5. At what time interval is the distance traveled by the car greatest? Explain.

SHARING OF ANSWERS INFRONT OF THE CLASS To summarize important points:

1. Speed is the rate at which object covers distance 2. The equation to calculate speed is v = d/t

3. A distance-time graph shows the distance traveled plotted against time 4. A faster speed is shown by a steeper line 5. When the line is horizontal the object is not moving.

CAN YOU ADD OTHER IMPORTANT CONCEPT?

THE END

Sourav aggarwal Xl-A

Isaac Newton, 1642-1727 In 1666, our old friend, Isaac Newton, was musing on the motions of heavenly bodies while sitting in a garden in Lincolnshire England, where he had gone to escape the plague then ravaging London.

What if the force of gravity, the same force that causes an apple to fall to the ground in this garden, extends much further than usually thought? What if the force of gravity extends all the way to the moon? Newton began to calculate the consequences of his assumption…

17-23

EVE D I S T A N C E

MAVIC

IDA

ROSE

TIME

The graph shows four beautiful runners. Basing from the graph, who is the winner? Why? Why do they have different shapes of graphline?

The possible graphs that could represent motion of a body are: 1. _________________________ d

t

2. __________________________ v t

d

Example: d(m) t(s) 50 10 100 20 150 30

200

150

2

100 1 50 t

0 0

Slope1 = y2-y1 x2-x1 Slope2 = y2-y1 x2-x1

10

20

30

=_______________________

=______________________

40

50

What did you notice about the computed slopes whose units are in m/s? _____________________ Since the speeds are the same, what kind of motion is shown in the straight-line d-t graph? __________________________

So, if the distance-time (d-t) graph is:

1. ____________________

2. ________________

3.

__________________

4.

__________________

5.

______________________

6. _______________________

7.

__________________________

8. ________________

9.

10.

________________________

________________________

From the different shapes of a d-t graph, a combination maybe possible to depict various changes in motion F

d D B

E C

G

0

A

H

t

Isaac Newton, 1642-1727 In 1666, our old friend, Isaac Newton, was musing on the motions of heavenly bodies while sitting in a garden in Lincolnshire England, where he had gone to escape the plague then ravaging London.

What if the force of gravity, the same force that causes an apple to fall to the ground in this garden, extends much further than usually thought? What if the force of gravity extends all the way to the moon? Newton began to calculate the consequences of his assumption…

17-12

Interpret the different points in the graph: 0-A

→___________________________

A-B

→___________________________

B-C

→___________________________

C-D

→___________________________

D-E

→___________________________

E-F

→___________________________

F-G →___________________________ Can you create a story out of the various graph lines?

Example:

MY WAY TO SCHOOL

I traveled with uniform speed (0-A) going to Nagtahan until I approached a stop light before the bridge so I stopped (A-B). Upon climbing the bridge I stepped on the gas pedal and the car accelerated (B-C). But a heavy traffic is building up in Lacson St. so I stopped (C-D). Finally I approached the high school building so I decreased the speed (D-E) but noticed that I left my bag, so, I drove back uniformly to Dapitan gate (E-F). Then I saw my son holding my bag along the street so I stopped (F-G) and got my bag.

Can you make your own story out of the various graphlines of a d-t graph? Were you in this situation before? You’re walking from your house in Lacson St. to the high school building. Upon reaching your classroom you noticed that the calculator you borrowed from your classmate was left at home and only your calculator is inside your bag. Your classmate is going to use it at 7am for your physics exam. No calculator, no exam! You decided to go back to your house since there is still enough time. Upon coming back you encountered an old woman who fainted near you. No other person in the vicinity

m1 m 2 F G 2 rˆ r The meaning of each term:

F: G: m1 : m2 : r2: rˆ :

Gravitational force on object 1 from object 2. –11 2 2 Universal gravitational constant = 6.673 x 10 N m /kg . Mass of object 1. Mass of object 2. Center distance from object 1 to object 2, squared. Unit vector from object 1 to object 2.

17-16

except you and the old woman. If you leave the old woman your classmate can take the test. If you assist her your classmate will get zero. What will you do and why? Are you accountable to any of them? ACTIVITY Choose your partner and sit together in one place. Get a graphing paper and write your names on it. Make a d-t graph showing at least 5 different graphlines and describe each. Write a story line out of the graphlines chosen.

ACTIVITY Choose a partner and sit together in one place. Prepare a graphing paper as your answer sheet Answer the questions in the activity sheet d D

25 20

E

15 C 10 5

A

B

F t

0

2

4

6

8

10

11

12

13

14

1. Is speed constant during any time interval? Explain. 2. At what time is the speed greatest? 3. At what time interval does the car go backward? Explain. 4. At which of the labeled points on the graph is the magnitude of the speed greatest? Explain. 5. At what time interval is the distance traveled by the car greatest? Explain.

SHARING OF ANSWERS INFRONT OF THE CLASS To summarize important points:

1. Speed is the rate at which object covers distance 2. The equation to calculate speed is v = d/t

3. A distance-time graph shows the distance traveled plotted against time 4. A faster speed is shown by a steeper line 5. When the line is horizontal the object is not moving.

CAN YOU ADD OTHER IMPORTANT CONCEPT?

THE END

Sourav aggarwal Xl-A

Isaac Newton, 1642-1727 In 1666, our old friend, Isaac Newton, was musing on the motions of heavenly bodies while sitting in a garden in Lincolnshire England, where he had gone to escape the plague then ravaging London.

What if the force of gravity, the same force that causes an apple to fall to the ground in this garden, extends much further than usually thought? What if the force of gravity extends all the way to the moon? Newton began to calculate the consequences of his assumption…

17-23