Kinematics in One Dimension: For GENERAL PHYSICS 1/ Grade 12 Quarter 1/ Week 3

 

KINEMATICS IN ONE DIMENSION for GENERAL PHYSICS 1/ Grade 12 Quarter 1/ Week 3

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OB JECT VE I VE S   At the end of this Self-Learni Self-Learning ng Kit, you should be able to:  K: identify the kinematic variables (distance, time, velocity, and acceleration) in a given set of conditions of a particle in motion;  S: construct graphs given sets of values;  values;   : solve simple problems involving uniform motion m otion and uniformly accelerated   and  A:motion; value the importance of graphs by understanding the pattern it conveys especially especiall y in telling patterns and relationships. 

NING LEAR NI NG  COMPETENC IES  Convert a verbal description of a physical situation involving uniform acceleration in one dimension into a mathematical description (STEM_GP12Kin-Ib12).   (STEM_GP12Kin-Ib12). Interpret displacement and velocity, respectively, as areas under velocity vs. time and acceleration vs. time curves (STEM_GP12KINIb- 14).  14).  Interpret velocity and acceleration, respectively, as slopes of positionvs. positionvs. time and velocity vs. time curves (STEM_GP12KINIb-15). 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). Solve for unknown quantities in equations involving one-dimensional uniformly accelerated motion, including free fall motion (STEM_GP12KINIb-17).   (STEM_GP12KINIb-17). Solve problems involving one-dimensional motion with constant acceleration in contexts such as, but not limited to, the ―tail-gating ―tail-gating phenomenon‖,   pursuit, rocket launch, and free- fall problems phenomenon‖, (STEM_GP12KINIb-19).   (STEM_GP12KINIb-19).

 

 

I. 

WHAT HAPPENED  PRE-ACTIVITY:    Activity:  ARE YOU MOVING OR NOT? N OT?   Directions: 1.  R ead  ead  and  study  the  topic  on  DESCR IBING   A ND  DEFINING MOTION below.  2.  Read and answer the guide questions in the Data Sheet.  3.  Draw conclusions based on the guide questions. 

DESCR IBING AN  AND DEFINING MOTION 

Let us consider this event. You were standing at the road side when a Ceres bus passed by. You noticed your classmate Pedro was sitting inside the bus travelling from Dumaguete City to Mabinay. You observed and surely your common sense will tell that Pedro was in motion.   Your observati observations ons a and nd conc conclusions lusions are val valid id and true that Pedro was iin n motion. There was a change in his position from your point of view. The location of Pedro (at some time) changed in an imaginary line. Hence, you can say that motion is a change in position or location of a particle as a function of time.  However, let us look at the same event event inside the Ceres bus where where Pedro is seated. Is Pedro in motion? Technically Pedro is not in motion. He is just sitting down. His position or location has not changed as a function of time. time. To an inside observer, Pedro is not in motion. If Pedro is not in motion but the bus is in motion, then it is possible that Pedro will be left from the bus.  bus.   How do you assess this situation ? How will you justify these valid and real observations ? What will be the improved or revised definition of motion ? What caused the different observations made regarding Pedro’s Pedro’s   location as a function of time? 

The following illustrations will provide a better picture of the situation.  

inside the Situation A. Situation  A. As the observer, you are outside the bus seeing Pedro inside bus.   bus.  

 

 

 

Situation B. The observer is inside the bus with Pedro on the front seat.

Based on the story you have read and illustrations you have seen, answer the questions found in the data sheet. Write your answers on your notebook/Answer Sheet using the format shown below.  

1.

Guide Questions  Questions   Responses/Answers Where were you standing when the bus passed by?  

2. Whom did you see inside the bus?   3. Was he seated inside the bus?  4. Can you say that your clas classmate smate wa wass iin n motion? Why ?  5. Did the observer inside the bus noticed that your classmate was just seated ?   6. Why do you thi think nk that your observa observation tion and the inside observer were NOT the  same?   7. Why did you see your cclassmate lassmate to be in motion while the inside observer did not ?   8. What is the difference in the point of reference or observation between you  you  and the inside observer?  9. Do you think tthis his was the rea reason son why you had different observations regarding the   apparent motion of your classmate?  10. What is motion? 

 

 

 

 

 A.  Velocity versus ver sus Time  Time  

In the Cartesian coordinate system, the y-axis will be designated as velocity in meters per second (m/s) while the x-axis x -axis will be designated as the time in seconds (s). The time and velocity of the moving particle is graphically shown below: 

The area in the above graph can c an be solved by multiplying its length by its width. Hence, if we use the formula,    Area = length shown as time (s)  x width shown as velocity (m/s) = m or simply

its displacement. displacement. Example:  A particle is moving at 10 m/s, what is its displacement after 20 s? 

 Area = length x width = 20 s x 10 m/s = 200 m is the variable displacement B. Acceleration  Acceleratio n versus Time  Time  

Using a similar line of thought as above, the graph below will be obtained. 

The area in the above graph can be solved by multiplying its length by its width. Hence, if we use the formula,    

 

 Area = length shown as time(s) x width shown as acceleration = m/s or its velocity.   velocity. Example:  A particle is accelerating at 3.0 m/s2, what is its velocity after 20 seconds? 

 Area = 20 s x 3.0 m/s2  = 60 m/s is the variable velocity C.  Position versus Time  

This time we apply the concept of the slope of the line generated between these two variables of a moving particle which are ar e position and time. The slope (m) of the generated line or curve will be obtained by dividing the y component with the x component.  Using the Cartesian coordinate system, the following figure can c an be obtained: 

Slope =

y component (m) ÷ x component (s) = m/s, which is the unit of measure for velocity (m/s)  (m/s) 

Example:   Example:

 A particle has moved from 0 to 30 m after 10 seconds. What is its velocity?  Using the graphical representations:  representations:  m = y/x = 30 m/ 10 s = 3 m/s which is the particle’s velocity  velocity   and represents graphically the slope of the  the   line

D.  Velocity Velocity versus ver sus Time  Time   

 

Using the slope (m) of the generated line from this relationship will yield acceleration. Similar procedure will be used in representing the interpretation.  interpretation. 

Slope (m) = y component ÷ x component = velocity (m/s) ÷ time (s) = m/s2

This will give us the physical quantity called acceleration in (m/s 2).  ).  Example:   Example:

 A particle is moving from 0 m/s to 20 m/s. After 10 seconds what is its acceleration? Using the formula to find the slope of the line, m = y component ÷ x component. m = (20 - 0) m/s ÷ (10 - 0) s = 2 m/s2 , which is a graphical representation of the linear slope and its corresponding physical  physical   quantity the acceleration. 

Here in the four different illustrations, we were able a ble to show how certain c ertain kinematic variables can be obtained using and interpreting graphical representations. 

Graph is very important important tool tool for effective effective and reliable conclusions that one may draw from its construction and geometry. It helps and facilitates in answering questions that can arise from the given set of graphed information.  information.  

 Velocity  Veloci ty is the change in position of a particle relativ relative e to time express expressed ed  

 

in meters per second while acceleration is the change in velocity of a moving particle with respect to time measured in meters per second squared. 

The abovementioned parameters can be shown graphically as you perform the tasks below. Be guided by the directions provided. Do this in a graphing paper. Answer the questions after each task on your notebook/Activity Sheet.   ACTI VI  VIT Y : Graphing   Materials needed:  

a.  Pencil with eraser   b.  Graphing or cross section papers   c.  Ruler d.  Calculator 

Procedure:

1.  2.  3.  4.  5. 

Get your pencil and graphing or cross section paper.  Plot the points using the tabulated values in the table below.   Use the x axis as the location of time as the independent variable.  Use the y axis as the location of position as the dependent variable.   Use your ruler to draw the approximate approximat e line of regression (the line that possibly connects the majority of the plotted points). p oints).  Time (s)  0 2 4 6 8 10 12 14 16

Position (m)  0 3 7 12 16 20 24 29 32

18 20

36 40  

 

6.  Choose any two points along the x axis and find its difference.  7.  Write this as delta X (∆X). (∆X).   8.  Choose any two points along the y-axis and find its difference.  9.  Write this as delta Y (∆Y). (∆Y).   10. Solve for the slope of the line by dividin dividing g ∆   Y by ∆  by ∆ X. X.   11. Write this value in your graphing paper as the slope of the line.  Questions:

1.  2.  3.  4. 

What does the slope of the line represent?  What is its unit of measure?  Choose another set of values for ∆  for ∆   Y and ∆  and ∆ X and solve for the slope?   Compare the results. Explain briefly your answer. answer.  

Procedure: 1.  Repeat the same procedure as in part 1 from Nos. N os. 3 to 11.  2.  Solve for the Velocity (position ÷ time) in the tabulated data below.  below.  3.  Write your corresponding answers in the spaces spac es provided in the table.  4.  Use the x axis as the location of o f time as the independent variable.   5.  Use the y axis as the location of velocity as the dependent variable.   6.   Answer the same questions 1-4 in Task Task No. 1. 1.  

Time (s)  0 2 4 6 8 10 12 14 16

Position (m)  0 3 7 12 16 20 24 29 32

18 20

36 40

 

 Velocity (m/s)  (m/s)  

 

Procedure: 1.  Repeat the same procedure as in part 1 from No. 3-11.   2.  Solve for the Acceleration (∆V (∆V ÷  ÷ ∆   ∆ t) t) or (V2- V1) ÷ t2  - t1) in the tabulated data below.  below.    3. Write corresponding answers in the column as shown in the table below.your  

Time (s) 

Position (m) 

0 2 4 6 8 10 12 14 16

0 3 7 12 16 20 24 29 32

18 20

36 40

 Velocity (m/s)  (m/s)  

Acceleration (m/s2) 

4.  Use the x axis as the location of time as a s the independent variable.  5.  Use the y axis as the location of acceleration as the dependent variable.  6.   Answer the same questions questions 1-4 in Task No. 1. 1.  

Expected Outputs: 

Task 1:

Graph

Task 2: Graph

 

Task 3: Graph

 

II. 

WHAT I HAVE LEARNED EVALUATION/POST-TEST  

MULTIPLE  CHOICE:  Choose  the  lett tter er   of   the  correct answer. wer.   Write  it in your notebook/Answer notebook/Answer Sheet. Show your solutions for items involving problem solving. 1.  Which of the following units of measure indicates kinematic variable ?  2

b. kg/s c. s/m d. m  a. m/g 2.  Which of these statements is (are) true?  1.  An  An obje object ct can hav have e zero acc accelera eleration tion and be at rest.  2.  An  An obje object ct can hav have e non nonzer zero o acce acceleration leration and be at res rest. t.  3.  An  An obje object ct can hav have e zero acc accelera eleration tion and be in mot motion. ion. 

a. 1 only b. 1 and 3 c. 1 and 2 d. 1, 2, 3  3  3.   A car is moving from rest and is uniform uniformly ly acceler accelerating ating at 2 m/s2. Which of the following statements is/are true ?  1.  The speed of the car will increase.  2.  The speed of the car will decrease.   3.  The acceleration of the car will increase.   4.  The acceleration of the car will decrease.  

a. 1

5. 

b.1 and 4

c. 2

d. 1 and 3 

4.  Two cars are traveling at the same speed and the drivers hit the brakes at the same time. The deceleration (slowing down) o off one car is double that of the other. By what factor do the times required for the two cars to come to as to differ ?  a.  twice as long c. one fourth as long  b.  half as long d. four times as long  long  Which of the following statements best describes acceleration?  a.  It is a change in the particle’s particle’s velocity  velocity per unit time.  time.   b.  It is apparent change in location/position of a moving particle with reference to its point of origin.  origin.  c.  It is the change in position (displacement) of a particle pa rticle as a function of time.  d.  It is the distance travelled as a function of time.  time.   6.   A pedicab travels in a straight line along the Kagawasan Avenue. Its distance  from a ―pasahero‖ is given as a function a  function of time by the equation 2 3 2 3  =    −    , where   = 1.50 m/s and   = 0.045 m/s . What is the average velocity of the pedicab for each interval at i. = 0s to = 2 s; ii. = 0s to = 4 s; iii. = 2 s to = 4 s? a. i. 2.80 m/s  m/s  ii.  5.28 m/s iii.  7.74 m/s

 

 

b. i. 2.88 m/s ii.  5.18 m/s iii.  9.77 m/s c. i. 2.80 m/s  m/s  ii.  5.29 m/s iii.  7.75 m/s d. i. 2.80 m/s ii.  5.28 m/s iii.  8.74 m/s 7.   A Visayan Visayan spotted spotted deer moving with constant acceleration covers a distance between two points 40.0 apart in 5.00 . Its speed as it passes the second point is 12.0 / . What is its speed at the first point ? a. 4.0 m/s b. 20.0 m/s c. 1.28 m/s2 d. 200 m/s2  Quarter 1 Week 3 Module 2: Kinematics problem solving 1. Georgia is jogging with a velocity of 4 m/s when she accelerates at 2 m/s2 for 3 seconds. sec onds. How fast is Georgia running now? 2. In a football game, running back is at the 10 yard line and running up the field towards the 50 yard line, and runs for 3 seconds at 8 yd/s. What is his current position (in yards)? 3. A cat is moving at 18 m/s when it accelerates at 4 m/s2 for 2 seconds. What is his new velocity? 4. A race car is traveling at +76 m/s when is slows down at -9 m/s2 for 4 seconds. What is his new velocity? 5. An alien spaceship is 500 m above the ground and moving at a constant velocity of 150 m/s upwards. How high above the ground is the ship after af ter 5 seconds? 6. A bicyclist is traveling at +25 m/s when he begins to decelerate at -4 m/s2. How fast is he traveling after 5 seconds? 7. A squirrel is 5.0 m away from f rom you while moving at a constant velocity of 3 m/s away from you. How far away is the squirrel after 5 seconds? 8. A ball is dropped off a very tall canyon ledge. Gravity accelerates the ball at 9.8 m/s2. How fast is the ball traveling after 5 seconds? 9. A bike first accelerates from 0.0 m/s to 5.0 m/s in 4.5 4. 5 s, and then continues at this constant speed for another 4.5 s. What is the total distance traveled by the bike? 10. A car traveling at 20 m/s when the driver sees a child standing in the road. He takes 0.80 s to react, reac t, then steps 2 on the brakes and slows at 7.0 m/s . How far does the car go before it stops? 11. A car starts 200 m west of the town square and moves with a constant velocity of 15 m/s toward the east. Draw a graph that represents the motion of the car a. Where will the car be 10 minutes later? b. When will the car reach the town square?

 

 

12. At the same time the car in #11 left, a truck was 400 m east of the town square moving west at a constant velocity of 12 m/s. a. Add the truck’s motion to the graph you drew for question #11.  #11.   b. Find the time where the car passed the truck. 13. A car is coasting backwards downhill at a speed of 3.0 m/s m/ s when the driver gets the engine started. After 2.5 s, the car is moving uphill at 4.5 m/s. assuming that uphill is positive direction, what is the car’s average acceleration? 2

14. A car slows from 22 m/s to 3.0 m/s at a constant rate of 2.1 m/s . How many seconds are required before the car is traveling 3.0 m/s? 15. An airplane starts from rest and accelerates at a constant rate of 3.00 m/s2 for 30.0 s before leaving the ground. a. How far did it move? b. How fast was it going when it took off? 16. A brick is dropped from a high scaffold. a. What is its velocity after 4.0 s? b. How far does the brick fall during this time? 17. A tennis ball is thrown straight up with an initial speed of 22.5 m/s. It is caught at the same distance above the ground. a. How high does the ball rise? b. How long does the ball remain in the air? 18. Consider the following velocity-time graph. 0 20 30 40 10 t (s) v (m/s) 0 2 4 10 6 8 12 Determine the displacement after t = ... a. 10 s. b. 20 s. c. 30 s. d. 40 s. 19. A bag is dropped for a hovering helicopter. heli copter. When the bag has fallen for 2.00 s, a. what is the bag’s velocity? b. how far has the bag fallen? 20. Bumblebee jumps straight upwards with a velocity of 14.0 m/s.What is his displacement of after 1.80 s? 21. A surprisingly spherical decepticon is rolled up a constant slope with an initial velocity of of 9.3 m/s.What is the acceleration of the decepticon if its displacement is 1.9 m up the slope after 2.7 s? 22. Optimus Prime coasts up a hill initially at 11.0 m/s. After 9.3 s he is rolling back down the the slope at 7.3 m/s. What is his acceleration? 23. Sonic (you know, the Hedgehog) rolls up a slope at 9.4 m/s. After 3.0 s he is rolling back down at 7.4 m/s. How far up the hill is he at this time? 24. Luigi jumps straight upwards at 1 15.0 5.0 m/s. How high is he when he is travelling travelling at: a) 8.0 m/s upwards? b) 8.0 m/s downwards?

Kinematics

Direction: Explain briefly. 1.  A honeybee leaves the hive and travels 2 km before returning. Is the displacement di splacement for the trip the same as the distance traveled? If not, why not?

 

 

2.  Two buses depart from Chicago, one going to New York and one to San Francisco. Each bus travels at a speed of 30 m/s. Do they have equal velocities? Explain. 3.  One of the following statements is incorrect. (a) The car traveled around the track at a constant velocity. (b) The car traveled around the track at a constant speed. Which statement is incorrect and why? 4.  At a given instant of time, a car and a truck are traveling traveli ng side by side in adjacent lanes of a highway. The car has a greater velocity than the truck. Does the car necessarily have a greater acceleration? Explain. 5.  The average velocity for a trip has a positive value. Is it possible for the instantaneous velocity at any point during the trip to have a negative value? Justify your answer. 6.  An object moving with a constant acceleration can certainly slow down. But can an object ever come to a permanent halt if its acceleration truly remains constant? Explain.