Philippine Christian University Physics 1 Grade 12 PDF

Philippine Christian University Sampaloc I, Dasmariñas City, Cavite, 4114 SENIOR HIGH SCHOOL...

Philippine Christian University Sampaloc I, Dasmariñas City, Cavite, 4114 SENIOR HIGH SCHOOL S.Y. 2024-2025 MODULE IN GENERAL PHYSICS 1 (GRADE 12) QUARTER 1 - WEEK 2 (AUGUST 12 – 16, 2024) LESSON 2: UNIFORM ACCELERATION AND FREE FALL MOTION Overview Kinematics is the study of how things move; that is how things move (distance and displacement), how fast they move (speed and velocity), the rate of change of velocity (acceleration), and how much time passes during the changes. The kinematic equations of motion which relate these quantities to each other. You learned the concepts of displacement, velocity, and acceleration in one dimension in the previous chapter. They are used to describe the motion of an object along a straight line, either along the horizontal or the vertical line. Seldom that we see objects moving with uniform velocity. We usually encounter bodies changing velocities from time to time. Speedometers are installed in cars and other vehicles to make sure the drivers are aware of the current velocity of the car they are driving. These are important for safety purposes. Cars and other vehicles often move and experience linear motion. Kinematic Equations. (n.d.). Pasco. Retrieved August 26, 2021, from https://studiousguy.com/free-fall-motion-examples/ https://www.pasco.com/products/guides/kinematic-equations Course Learning Outcome Explain the different properties and basic concepts of Kinematics, its measurement, calculations and interpretation of how it applies in one and two dimensions. Analyze the effects of different forces in motion such as gravitational, normal, and frictional force to utilize the free-body diagrams to represent forces and solve problems involving the net force and acceleration of objects. Define and explain Newton's Law of Universal Gravitation and how the gravitational force between two masses governs the motion of celestial bodies. Apply knowledge and understanding of kinematics and the different laws of motion to systematically predict resulting motion in different problem-solving activities. Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 1  Analyze the properties and behavior of waves including wavelength, frequency, amplitude, and speed to distinguish between different types of waves (mechanical, electromagnetic, transverse, and longitudinal) and how it transfers energy. Illustrate the parts and structure of the different types of waves. Demonstrate knowledge and comprehension of thermodynamics by citing and giving examples of how it is observed in real life scenarios. Lesson Objectives At the end of this lesson, you are expected to: Differentiate vector and scalar quantities; Perform addition of vectors; Rewrite a vector in component form; Convert a verbal description of a physical situation involving uniform acceleration in one dimension into a mathematical description; Interpret displacement and velocity, respectively, as areas under velocity vs. time and acceleration vs. time curves; Interpret velocity and acceleration, respectively, as slopes of position vs. time and velocity vs. time curves; 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. Solve for unknown quantities in equations involving one-dimensional uniformly accelerated motion , including free fall motion; Solve problems involving one-dimensional motion with constant acceleration in contexts such as, but not limited to, the “tail-gating phenomenon”, pursuit, rocket launch, and free-fall problems; Differentiate acceleration from speed; Calculate the velocity, displacement, and time of an object; and Reflect on the importance of having a knowledge regarding acceleration to apply on real life situations. You may copy and paste the link then enter to the search engine to play video/s: https://youtu.be/vxFYfumAAlY Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 2  Essential Questions What is the relationship between speed, time, and distance? How does it affect each other? How can we relate or use the concept of acceleration in your current and past experiences as a student? What is the importance of understanding the concept of free-falling motion in the fields of engineering, sports, construction, and other fields outside the field of science? In what way can you utilize your knowledge about free fall and uniformly accelerated motion in your daily life? Test Yourself 1. What is acceleration? _____________________________________________________________________________________ _____________________________________________________________________________________ 2. What’s the difference between velocity and speed? _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Study These Terms On this module, you will encounter these important terms: Distance - can be defined as total length moved. If you run around a circular track, you have covered a distance equal to the circumstance of the track. Distance is a scalar, which means it has no direction associated with it. Displacement - is a vector, representing a change in position. Displacement is defined as the straight-line distance between two points. Velocity - of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 3  Speed - can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed. Acceleration - is a vector quantity that is defined as the rate at which an object changes its velocity. Free fall - is any motion of a body where gravity is the only force acting upon it. Lesson Proper Distance and Displacement Image: Distance and displacement https://socratic.org/questions/what-is-the-difference-between-distance-and-displacement SI unit: meter (m) Distance can be defined as total length moved. If you run around a circular track, you have covered a distance equal to the circumstance of the track. Distance is a scalar, which means it has no direction associated with it. Displacement, however, is a vector, representing a change in position. Displacement is defined as the straight-line distance between two points. The displacement is denoted by the symbol x , and is given by x = x − x Where the initial position of the car is labeled x and the final position is x. The Greek  stands for “change in” or final quantity minus the initial quantity. Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 4  Speed and Velocity Image: Velocity and Speed https://www.quora.com/If-the-speed-of-an-object-is-zero-its-velocity-must-also-be-zero-Do-you-agree-with-this-statement Average speed is defined as the total distance a moving objects covers divided by the total time it takes to cover that distance. Where s stands for speed, d is for distance and t is time. SI unit: meter per second ( m / s ) Example Anton wants to exercise so he ran 200m in 90s. Find her average speed. We have to find her average speed for the whole run. The distance and time is known so we can simply substitute the given to the equation d s= t 200𝑚 𝑠= 𝑠 = 𝟐. 𝟐𝟐𝒎/𝒔 90𝑠 Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 5  Velocity The terms speed and velocity are interchangeable. Speed is scalar quantity while velocity is a vector quantity. Hence, the velocity gives considerably more information than speed. Average speed is the total distance divided by the total time, average velocity is the change in position or the displacement divided by the change in time: 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑇𝑖𝑚𝑒 ∆𝑑 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = ∆𝑡 SI unit: meter per second (m/s) Speed, which is always positive since speed is scalar quantity but the average velocity of an object in one dimension can either be positive or negative, depending on the sign of the displacement. Velocity-Time Graphs On a velocity-time graph a horizontal (flat) line indicates the object is travelling at a constant speed. A straight diagonal line indicates the object's velocity is changing. In the graph on the left, the line sloping upwards shows the object is accelerating and the line sloping downwards in this case towards v = 0, shows it is decelerating. The negative value of the gradient gives the negative value for the acceleration (or deceleration), BUT, a negative value does not always mean slowing down! See the next section on 'DIRECTION VECTORS' for elaboration. https://www.pathwayz.org/Tree/Plain/VELOCITY-TIME+GRAPHS Be careful here. The general rule of thumb is if the object is going from a high speed to a low speed, it is decelerating. Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 6  VECTORS A vector quantity is a quantity that is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity that is fully described by its magnitude. The emphasis of this unit is to understand some fundamentals about vectors and to apply the fundamentals in order to understand motion and forces that occur in two dimensions. Examples of vector quantities that have been previously discussed include displacement, velocity, acceleration, and force. what is motion in physics? The concept of displacement and distance. (2021, January 22). Downlaod Physics App - The Best Physics App 2021. https://towardbrightspark.info/what-is-motion-in-physics-the-concept-of-displacement-and-distance/ In contrast to vectors, ordinary quantities that have a magnitude but not a direction are called scalars. For example, displacement, velocity, and acceleration are vector quantities, while speed (the magnitude of velocity), time, and mass are scalars. VECTOR ADDITION Two vectors can be added together to determine the result (or resultant). Recall in Newton's laws of motion, that the net force experienced by an object was determined by computing the vector sum of all the individual forces acting upon that object. That is the net force was the result (or resultant) of adding up all the force vectors. During that unit, the rules for summing vectors (such as force vectors) were kept relatively simple. Observe the following summations of two force vectors: Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 7  The Pythagorean Theorem The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors that make a right angle to each other. The method is not applicable for adding more than two vectors or for adding vectors that are not at 90-degrees to each other. The Pythagorean theorem is a mathematical equation that relates the length of the sides of a right triangle to the length of the hypotenuse of a right triangle. Sample Problem: Jake leaves the base camp and hikes 15 km, north and then hikes 15 km east. Determine Jake's resulting displacement. Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 8  Using Trigonometry to Determine a Vector's Direction The direction of a resultant vector can often be determined by use of trigonometric functions. Most students recall the meaning of the useful mnemonic SOH CAH TOA from their course in trigonometry. SOH CAH TOA is a mnemonic that helps one remember the meaning of the three common trigonometric functions - sine, cosine, and tangent functions. These three functions relate an acute angle in a right triangle to the ratio of the lengths of two of the sides of the right triangle. From the example earlier, let us look for the direction of the magnitude: Once the measure of the angle is determined, the direction of the vector can be found. In this case the vector makes an angle of 45 degrees with due East. Thus, the direction of this vector is written as 45 degrees Acceleration We can change the state of the motion of an object by changing its speed, its direction of motion, or both. Any of these changes is a change in velocity. Sometimes we are interested in how fast the velocity is changing. A driver on a two-lane road who wants to pass another car would like to be able to speed up and pass in the shortest possible time. The rate which the velocity is changing is called acceleration. Acceleration is rate, it is measure of how the velocity is changing with respect to time: v a= t 2 SI unit: meter per second squared ( m / s ) Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 9  Example Jennie is driving her car that is moving initially at 20 m/s accelerated up to 50 m/s during the time of 7 seconds. Find the acceleration of the car. We have to find the acceleration. The time t, initial position xi and final position xf are given and time known so we can simply substitute the given to the equation. ∆𝑣 𝑣𝑓 − 𝑣𝑖 𝑎= = ∆𝑡 𝑡𝑓 − 𝑡𝑖 𝑚 𝑚 50 − 20 𝑠 𝑠 𝑎= 7𝑠 𝑚 30 𝑠 𝑎= 7𝑠 𝑎 = 𝟒. 𝟐𝟗 𝒎/𝒔𝟐 In physics, the term acceleration applies to decreases as well as increases in speed. This is often called deceleration, or negative acceleration. We experience deceleration when the driver of a bus or jeepney slams on the brakes and we tend to hurtle forward. One Dimensional Motion with Constant Acceleration A lot of applications in mechanics involve objects moving with constant acceleration. When an object moves with constant acceleration, the acceleration does not change through a manner of motion. Kinematics Equations with constant acceleration 𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡 𝑣𝑖 + 𝑣𝑓 𝑥𝑓 − 𝑥𝑖 = ( )𝑡 2 1 𝑥𝑓 = 𝑥𝑖 + 𝑣𝑖 𝑡 + 𝑎𝑡 2 2 𝑣𝑓 2 = 𝑣𝑖 2 + 2𝑎(𝑥𝑓 + 𝑥𝑖 ) Where t is time, vi is the initial velocity, vf is the final velocity, a is the acceleration, initial position is xi and the final position is xf. When solving problems using the kinematics equations, it is helpful if we will draw the problem and write down the given quantities and the quantities we want to find. Furthermore, the best way to gain confidence in the use of these equations is to work on a number of problems. Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 10  Example A truck starting from the rest accelerates at a constant rate of 8.00 m/s2. What is the final velocity of the truck after it has travelled 2.00 x 102 ft? We’d like to find the velocity v after a certain known displacement x. The acceleration a is also known, as is vo the initial velocity , so the Eq. 4.8 looks most useful. The rest is simple substitution. Convert units of x to SI. 1𝑚 2.00𝑥102 𝑓𝑡 = (2.00𝑥102 𝑓𝑡) ( ) = 60.98𝑚 3.28𝑓𝑡 Use the kinematics equation for final velocity: 𝑣𝑓 2 = 𝑣𝑖 2 + 2𝑎(𝑥𝑓 + 𝑥𝑖 ) Solve for v , taking the positive square root because the car moves to the right: 𝑣𝑓 = √𝑣𝑖 2 + 2𝑎(𝑥𝑓 + 𝑥𝑖 ) Substituting the values: 𝑚 𝑚2 𝑣𝑓 = √𝑣𝑖 2 + 2𝑎(𝑥𝑓 + 𝑥𝑖 ) = √(0) + 2 (8.00 ) (60.98𝑚 + 0𝑚) = √975.68 𝑠2 𝑠2 𝑣𝑓 = 𝟑𝟏. 𝟐𝟒 𝒎/𝒔 Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 11  Free Fall A billiard ball fell from a table. Does it accelerate while falling? Gravity causes the billiard ball to accelerate downward once it begins falling. In real life, air resistance affects the acceleration of a falling object. Let’s imagine there is no air resistance and that gravity is the only thing affecting a falling object. Such an object would then be free fall. Freely falling objects are affected only by a gravity. The constant acceleration of a freely falling body is called the acceleration due to gravity, and we denote its magnitude with the letter g. We will frequently use the approximate value of g at or near the earth’s surface: m g = 9.8 s2 Formulas in this topic will still be the same as that of the Linear Motion. You just replace the variables x (distance) to y (height) and a (acceleration) to g (gravitational constant). v = vo + gt Eq. 4.9  v + gt  y− y = o t  2  Eq. 4.10 1 2 y = yo + vo + gt 2 Eq. 4.11 v 2 = v02 + 2 g ( y − y0 ) Eq. 4.12 Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 12  Example A mango falls from a branch 15 m above the ground. a) How long until the mango touches the ground? b) With what speed in meters per second does it strike the ground? yo = 0 vo = 0 At initial height , the initial velocity is as well. Since the motion is free fall the acceleration is also 2 known which is equal to 9.8m / s. We want to find the time t. And it looks like Eq. 4.11 is the proper equation to use. 1 2 y = yo + vot + gt 2 yo = 0, vo = 0 Substituting and solve for t by manipulating the equation we have: 1 2 y = 0 + (0) + gt 2 2y t= g Substituting y = 15 m and g = 9.8m / s : 2 2(15m) t= 9.8m / s 2 t = 1.75 s We can find the velocity v at this time by using Eq. 4.9 v = vo + gt v o = o g = 9.8 m / s 2 Substituting , and t = 1.75 s we find: v = 0 + (9.8m / s 2 )(1.75 s ) v = 17.15 m / s Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 13  Summary Motion refers to the characteristics of the movement of an object or body. The basic components of motion are speed/velocity, distance/displacement, time, and acceleration. These components are important to determine the nature of an object in motion and how can we quantify it. Speed (Scalar) and Velocity (Vector) refers to how fast an object moves. Its basic unit of measurement is meters per second (m/s). Distance (Scalar) and Displacement (Vector) on the other hand, is the total length the object in motion has travelled. Acceleration is the change of rate of speed/velocity of an object. If the acceleration of an object is positive, the moving object is speeding up. If the acceleration is negative, it means that the object is slowing down. If the acceleration is zero, it means the object is at rest or at a constant speed. If an object is falling without any assistance of external force and only gravity is applied, the object is in Free Falling Motion. Free fall refers to the downward motion of an object due to the effect of gravitational force. Free-falling objects are subjected to a constant acceleration of 9.8m/s2 due to earth’s gravity. Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 14  Activity #2 (Performance Task 1) NAME: STRAND & SECTION: DATE/WEEK NO.: SCORE: / 100 LABORATORY VELOCITY INTRODUCTION In everyday usage, the terms “speed” and “velocity” are used interchangeably. In physics, however, they are distinct quantities. Speed is a scalar quantity and has only magnitude. Velocity, on the other hand, is a vector quantity and so has both magnitude and direction. This distinction becomes more apparent when we calculate average speed and velocity. Average speed is calculated as the distance traveled over the total time of travel. In contrast, average velocity is defined as the change in position (or displacement) over the total time of travel. The average velocity of an object does not tell us anything about what happens to it between the starting point and ending point, however. For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he gets to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals. OBJECTIVE Demonstrate the validity of the formula discussed in the lesson about Velocity. MATERIALS Marble/coin Measuring tape Paper Pencil Stopwatch. Estimated Time Frame: 30 minutes PROCEDURE 1. Measure a distance of 200 cm from the ground. Drop that point, drop the marble. 2. Using the knowledge you obtained from the lesson, compute of the time it took for the marble to hit the ground and its velocity. 3. Go back and measure 200 cm from the ground once more. Drop the marble from that point and this time use a stopwatch to measure the elapsed time for the marble to hit the ground. 4. Compare the result of your computation from the result of the stopwatch. Present your findings by answering the given guide questions. Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 15  DATA AND RESULTS After conducting the activity, write the data and results you obtained below: 2y Formula for Time (s): t = g Note: use the given values for the computation. Formula for Velocity (𝑚⁄𝑠): v = vo + gt Note: use the obtained value of time from the previous computation. Time(s) elapsed by the object from initial to final position (USING STOPWATCH): Formula for Velocity (𝑚⁄𝑠): v = vo + gt Note: use the obtained value of time from the stopwatch. Guide Questions: 1. Using the data you’ve collected from the activity, was there a difference from the magnitude of time you attained from using the formula given from the one you got from using a stopwatch? Explain your answer. 2. Based on the result of your activity, can we say that the discussed formulas were accurate? 3. What is the relationship of time, distance, speed, velocity and acceleration? Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 16  Rubric for Scoring: Score Description Presents a clear, focused thesis/main idea; demonstrates thorough, accurate content knowledge; 90-100 provides substantial, relevant evidence; offers insightful analysis and effective explanations; and organizes ideas in a clear, logical manner using precise, engaging language. Presents a clear thesis/main idea; demonstrates good content knowledge with few inaccuracies; 80-89 provides appropriate evidence; offers sound analysis and clear explanations; and organizes ideas in a generally clear and coherent manner using clear, appropriate language. Presents a basic thesis/main idea; demonstrates limited content knowledge with several 76-80 inaccuracies; provides limited or somewhat irrelevant evidence; offers basic analysis and limited explanations; and organizes ideas in a somewhat unclear manner using basic language. Lacks a clear thesis/main idea; demonstrates limited content knowledge with significant errors; 70-75 provides little to no evidence; offers weak or flawed analysis and inadequate explanations; and organizes ideas in a confusing manner using vague, inappropriate language. Supplemental Readings and Materials Introduction to free fall motion. (n.d.). https://www.physicsclassroom.com/class/1DKin/Lesson-5/Introduction Kinematic equations and free fall. (n.d.). https://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic- Equations-and-Free-Fall Learning Resources Caintic, H. (2017). General Physics 1 for Senior High School. C & E Publishing, Inc. Sayson, L., Navalta, C. (2015). Physics 1 Workbook. Mindshapers Co., Inc. Prepared by: Checked By: Noted By: Eleze Abraham P. Ambrad, LPT. Angela A. Zarcilla, LPT. Maria Beatriz B. Sico, MM Subject Lead Teacher – Principal Marie Elaine B. Caparas, MAEd, LPT. Science 12 John Karlo C. Narvaez, LPT. Robin C. Padon, LPT. Vanessa C. Pedro. Subject Teacher/s Disclaimer: This module is adapted and modified from the source materials listed in the references list. This is an exclusive property of Philippine Christian University-Dasmariñas SHS and is provided only to enrolled students for their academic use. This module is provided for free by the school through softcopy and/or printed media. Reproduction of this module without official permission is prohibited. 17