Grade 5 Science Unit 8 Motion Study Guide PDF

Unit 8 Motion Table of Contents Table of Contents 1 Introduction 3 Essential Questions 4 Review 4 Lesson 8.1: Descrip...

Unit 8 Motion Table of Contents Table of Contents 1 Introduction 3 Essential Questions 4 Review 4 Lesson 8.1: Descriptors of Motion 5 Objectives 5 Warm-Up 5 Learn about It 6 Key Points 11 Web Links 11 Check Your Understanding 12 Challenge Yourself 13 Lesson 8.2: Measuring Distance and Time 14 Objectives 14 Warm-Up 14 Learn about It 15 Key Points 19 Web Links 19 Check Your Understanding 19 Challenge Yourself 22 Lesson 8.3: Calculating Speed and Velocity 23 Objective 23 Warm-Up 23 Learn about It 24 Worked Examples 26 Key Points 32 Web Links 32 Check Your Understanding 33 1  Challenge Yourself 34 Lesson 8.4: Calculating Acceleration 35 Objective 35 Warm-Up 35 Learn about It 36 Worked Examples 38 Key Points 41 Web Links 41 Check Your Understanding 42 Challenge Yourself 43 Laboratory Activity 44 Performance Task 45 Self Check 47 Key Words 47 Key Formula 48 Wrap Up 49 Photo Credits 49 References 50 2 GRADE 5 | SCIENCE Unit 8 Motion In a running competition, racers position themselves first in the starting line. As the gun is fired, the race will start and racers run as fast as they can to reach the finish line. Some runners may be behind others who are running fast, while those who are ahead may reach the finish line first. Based on the scenario, how can you say that the runners are in motion? What are some words that can be used to describe their movements? Motion is a change in the position of an object over time. An object changes its position when force is applied to it. There are different ways to describe the motion of an object. In this unit, you will learn the different descriptors of motion and how they can be measured and calculated. 3  Essential Questions At the end of this unit, you should be able to answer the following questions. How will you describe motion? What are some tools used to measure distance and time? What are the standard units in expressing distance and time? What is the difference between distance and displacement? How is velocity different from speed? How do you compute for speed and velocity? How do you compute for the acceleration of a moving object? Review Force is a push or a pull on an object. It can change the shape, size, or form of an object. An applied force can also move an object initially at rest. It may also speed up or slow down a moving object. Force may be classified as a contact force or a noncontact force. ○ A contact force is a kind of force that requires physical contact between the interacting objects. Friction is an example of a contact force. ○ A noncontact force is a kind of force that acts between interacting objects even if they are physically separated. Gravitational force and magnetic force are both examples of noncontact forces. 4  Lesson 8.1: Descriptors of Motion Objectives In this lesson, you should be able to: enumerate different terms that are used to describe motion; differentiate distance from displacement; differentiate speed from velocity; and interpret a map to determine distances and displacements when traveling. Look around and observe the things around you. You will see different objects in motion such as running vehicles, rustling leaves, and waving hanged clothes. Such movements are caused by force applied to each object. How can one describe the motion of an object? Warm-Up Bottle Caps Battle Materials: 10 identical plastic bottle caps table with a smooth surface Procedure: 1. Play this activity with a partner. 2. Each player must have 5 plastic bottle caps that are identical. One player must place the bottle caps on one edge of the table. The other player must place the bottle caps on the other edge. 5  3. The objective of the game is to hit the bottle caps of the opponents and let them fall off the table. To do this, you have to flick your own bottle cap and target your opponent’s bottle cap. 4. Take turns in hitting the bottle caps. The person with more bottle caps remaining on the table wins the game. Guide Questions: 1. What happens to the bottle cap when you flicked it with your fingers? 2. How will you describe the movement of the bottle cap when you exert more force as you flick it? 3. Why do some bottle caps do not fall off the table easily? Learn about It Frame of Reference You have learned that motion is a change in the position of an object over time. The motion of an object can be determined by observing it at a specific frame of reference or a fixed point of position. Therefore, to completely define the motion of an object, one should note the change in its position over time in relation to the frame of reference. For example, the frame of reference in the illustration below is the edge of the table shown as point A. Since the ball’s position did not change with respect to the frame of reference, the ball is motionless, at rest or stationary. 6  Fig. 1. The ball is said to be at rest when it does not change its position with respect to the frame of reference. On the other hand, when the ball slowly rolled towards the edge of the table, shown below as point B, the ball moved away from the frame of reference which is point A. This shows that the ball was in motion when it rolled from point A to point B. Fig. 2. The ball is said to be in motion when it changed its position from point A to point B. Motion Descriptors Motion descriptors are words used to describe objects that are in motion. There are different ways to describe motion. Distance tells how far two objects (or points) are from one another. It describes the total space covered by a moving object. It is usually expressed in centimeters, meters, and kilometers. Displacement is distance with direction. It refers to how far an object travelled with respect to a frame of reference. It is the shortest distance covered by an object from the initial to its final position. Similar to distance, it is also expressed in centimeters, meters, and kilometers but with a specified direction. 7  Fig. 3. The total distance covered from point A to point E is 35 meters while the displacement is 15 meters. Time is also an essential factor in describing motion. It refers to the duration of a period or how long an object is moving. Time is expressed in seconds, minutes, hours, or days. It plays an important role in determining how fast or slow a moving object is. Speed refers to the rate of change in the position of a moving object. It measures how fast an object moves. It is calculated by determining how much distance was covered by a moving object over a certain period of time. On the other hand, velocity is the speed with direction. It refers to the rate of change in the position of a moving object with respect to a frame of reference. It describes how fast and in what direction an object is moving. The velocity of an object is computed by dividing displacement by time. Lastly, acceleration is the rate of change in velocity over a certain period of time. When there is a change in velocity, there is acceleration. Change in velocity occurs when a moving object speeds up, suddenly stops, or makes a turn. An object speeding up is experiencing acceleration while an object slowing down is undergoing deceleration. Acceleration is calculated by dividing the change in velocity by the change in time. 8 Interpreting Maps Maps are highly useful tools in locating yourself in a specific place. Maps also serve as guides when travelling from one place to another. Reading a map is an important skill in determining distances and displacements. Study the map below. What could be the shortest and farthest distance that Rick will have to travel from his house to school? To solve this, you have to analyze first the distances between each location to Rick’s house. Knowing the direction to take as one travel’s will also help determine the shortest distance to take. For instance, if Rick will go East from his house, he only has to walk 8 meters to reach his school. On the other hand, if he decides to go South then turn East before going North to his school, he will cover 18 meters to reach his destination. The illustration below shows Rick’s shortest and farthest routes from his house to school. 9 The distances that a person covers when travelling may vary, but the displacement remains the same as long as the initial position is the same. For instance, the longest distance that Rick will travel to reach his school is 18 meters. But the displacement or the shortest distance that he covered from the initial position (his house) to the final position (the school) is just 8 meters East as shown on the illustration below. When travelling, one can take many directions with varying distances. For instance, there are two possible routes if Rick would like to visit Glenn in his house. First, he can go East then turn South when he reaches the school, then go a little East until he reaches Glenn’s house. Alternatively, he can go South first then turn East when he reaches Daryl’s house. 10  Key Points Motion refers to the change in the position of an object in relation to the frame of reference or fixed point. Motion of an object can be described using its different descriptors: ○ Distance describes the total space covered by a moving object. ○ Displacement is distance with direction. It is the shortest distance covered by an object from the starting point to its final point. ○ Time refers to how long an object is moving. ○ Speed refers to the rate of change in the position of a moving object. ○ Velocity is the speed with direction. It refers to the rate of change in the position of a moving object with respect to the frame of reference. ○ Acceleration is the rate of change in velocity over a certain period of time. Web Links For further information about descriptors of motion, you can check the following web links: Watch this video to learn more about the differences between distance and displacement. The Science Classroom. 2013. ‘Distance and displacement.’ https://www.youtube.com/watch?v=V8hJhTE3bUk Read this article to learn more about the position and displacement. cK-12.org. 2018. ‘Position and Displacement.’ https://www.ck12.org/c/physics/position-and-displacement/lesson/Position-and-Disp lacement-PHYS/?referrer=concept_details Watch this video to understand the differences between distance and displacement. ParticleMen. 2009. ‘They Might Be Giants - Speed and Velocity.’ https://www.youtube.com/watch?v=DRb5PSxJerM 11  Check Your Understanding A. Read and analyze the following statements given. Identify what is being asked in each statement. 1. It is the rate of change in the position of a moving object. 2. It refers to the rate of change in velocity of an object over a period of time. 3. It describes the duration of a period or how long an object is moving. 4. It is a term used for an object that is at rest or motionless. 5. It refers to the distance with direction. B. Identify the motion descriptor that is shown in each situation. 1. The boy is 15 steps away from the ball. 2. It took the runner 5 minutes to reach the finish line. 3. The shortest route going to the lavatory is 35 steps forward. 4. The dog runs 5 meters in 10 seconds. 5. The ambulance slows down as it reaches the emergency area of the hospital. C. Use the image below to answer the following questions. 12  1. What is the distance between the house and tree C? 2. What is the distance between the house and tree A? 3. What is the total distance that will be covered by the biker if he started from tree A, passed by the house, then turned right to tree C? 4. What is the displacement of tree A and tree C? 5. To what direction does the biker have to travel to reach tree C faster? Challenge Yourself Answer the following questions briefly. 1. What is the importance of the frame of reference in describing the motion of an object? 2. How will you know if the given measurement pertaining to motion is a distance or displacement? 3. Why do objects move in different directions? 4. How does understanding the concept of distance and displacement be beneficial for a student like you? Provide a concrete example to support your answer? 5. What do you think will happen if all objects move at the same time and in the same direction? 13  Lesson 8.2: Measuring Distance and Time Objectives In this lesson, you should be able to: describe the motion of an object by tracing and measuring its change in position (distance traveled); describe the motion of an object based on the length of time it traveled; enumerate tools that are used to measure distances; and use appropriate measuring tools and correct standard units. It is easy to say that an object is distant when it is out of your reach. In contrast, an object that you can easily grasp is described to be near. Also, fast and slow-moving objects are set apart using the time component of their motion. How do you quantify or measure distance and time? Warm-Up Longest Line Materials: meter stick digital timer Procedure: 1. Form a group of five. Using the accessories that you are wearing (i.e. shoes, shoelaces, etc.) form the longest possible line on the floor. 2. Assign one member of the group to record the time it took for your group to form the longest line. Stop recording the time once all the group members put their accessories on the line. 3. Measure the length of the line using a meterstick. Start from the end of the first accessory you put on the floor to the end of the last accessory. 14 Guide Questions: 1. How long is the line that you formed on the floor? 2. How did you measure its length? 3. Why do you have to measure from end to end? 4. How long did it take for your group to form the longest line? 5. How did you measure time in this activity? Learn about It To measure means to provide the exact size or quantity of an object or event using instruments with standard units. For example, instead of saying that the distance is far, it can be measured using a ruler or a meter stick and express it in meters or kilometers. Instead of saying that an event took so long, time may be recorded using a stopwatch or a clock and express it in seconds or minutes. Measuring Distance There are different instruments used in measuring distance. The most common tool in determining short distances or length is the ruler. It may come in various shapes and sizes, but its standard units are expressed in millimeters (mm), centimeters (cm), or inches (in). Fig. 4. The lines above the ruler represent centimeters while the lines below show inches. A meter stick can measure distances up to one meter. It is usually marked in millimeters and centimeters. It is highly useful in measuring distances longer than a ruler. A yardstick often appears as a flat, thin and rectangular wood or metal. It measures objects up to a yard which is equivalent to 3 feet long. A measuring tape is used for distances that are also too long for a ruler. Its main advantage is that it is very flexible and can be used around corners or curves. On the other 15 hand, an odometer is used for huge distances such as those covered by vehicles. This instrument expresses distance in kilometers (km) or miles (mi). The odometer is usually installed on the car’s dashboard. It is for the driver to easily monitor the distance or mileage that the car has covered. This will give the driver an idea how much it has travelled already and if it has exceeded the maximum mileage it could cover since its manufacturing date. Fig. 5. Measuring tape (left) comes in compact size but can be stretched longer to measure long distances. Odometer (right) is usually seen on the dashboard of a car, which tells the total distance it travelled in a digital or a manual counter. The distance between two points may be determined using a proper measuring tool. Suppose a ball rolled from point A to point B, as shown in the figure below. Assuming that the distance covered by the ball is small, a ruler would be appropriate to measure the distance between the two points. Fig. 6. The distance between point A where the ball was initially at rest and point B where the ball rolled and stopped is 16 centimeters. 16 Here are the steps in measuring distance using a ruler: 1. Place the ruler on the surface where the points are located. 2. Align the zero mark of the ruler to point A which is the ball’s initial position. 3. Locate point B on the ruler or the position where the ball stopped rolling. 4. The reading where point B lies on the ruler is the distance covered by the ball. The procedure for measuring short distances is similar to measuring long distances. The only difference is the tool used for measuring, especially if there is a required unit of measurement to be used. For example, it is not appropriate to use a ruler in measuring the distance between two cities. An odometer is used instead for this specific purpose. On the other hand, a meterstick may be used instead of a ruler to measure the distance between two students standing in the same classroom. This will make the process of measuring easier and faster. Measuring Time Time can be measured using an ordinary clock or watch, a digital timer, or a stopwatch. Such instruments express time in seconds (s), minutes (min), and hours (h). A stopwatch is a special kind of watch that can be digital or analog. It has start, stop, and reset buttons that are used to determine the exact duration of simultaneous events such as races. It helps in identifying who finished a certain task in a shorter amount of time. Although it is a common instrument used in sports, it is also found in laboratories, quiz bee competitions, and examinations. Fig. 7. A clock may come in analog or with moving hands (left) or in digital (right) form. 17 In reading the time on an analog clock, it is important to distinguish its different hands and their purpose. The short hand is known as the hour hand as it tells the hour, while the long hand is the minute hand which tells the minutes that pass by. There is another thin, long hand that moves the fastest as it tells the number of seconds. An analog clock is divided into 12 sections. Each number on each section represents a specific hour. Between those numbers are tiny marks or lines wherein each mark is equivalent to 1 minute. The distance between each number is 5 minutes and the total number of minutes in a regular clock is 60 minutes. To read the time on the clock, start first with the short hand to tell the hour. Then, count the number of minutes by determining where the long hand is pointing. Fig. 8. An analog clock has three hands – the short hand for hours, long thick hand for minutes, and long thin hand for second. The time shown on the clock above is 1 hour and 50 minutes or 1:50. An analog clock may also be used in counting the time in seconds. Each movement of the second hand is equivalent to one second. Similarly, every one mark that the second hand passes counts as one second. One complete trip around the clock of the second hand is sixty (60) seconds which is equivalent to one minute. 18  Key Points Distance may be measured using a ruler, meter stick, yardstick, measuring tape, or odometer. Shorter distances may be expressed in centimeters or inches while longer distances are expressed in meters, kilometers, feet, yards, or miles. Time may be determined using a clock, watch, timer, or stopwatch. Such devices may be in the form of analog digital. Web Links For further information on measuring distance and time, you can check the following web links: Watch this video to learn how sundials are used to know the time of a day. Canada Science and Technology Museum. 2009. ‘Sundials.’ https://www.youtube.com/watch?v=tI0GqYJha1Q Read this article to know how to make your own sundial. Maegan Arnett. 2018. ‘It’s about Time… To Make a Sundial!’ https://www.scientificamerican.com/article/its-about-time-to-make-a-sundial/ Check Your Understanding A. Read and analyze the following situations given. Identify the most appropriate tool to measure the distance or time in each situation. 1. Sasha wants to know how far her seat is from the classroom door. 2. Eugene wants to know how long it will take him to run a race track. 3. Maggie wants to determine the length of her notebook. 4. Carol wants to know how far her car has travelled. 5. Carl wants to know the duration of his travel from his house to school. 19 B. Read the measurement of distance (length) in each illustration. 1. 2. 3. 4. 5. B. Read the measurement of time in each illustration. 1. _________________________________ 20 2. _________________________________ 3. _________________________________ 4. _________________________________ 5. _________________________________ 21  Challenge Yourself Answer the following questions briefly. 1. How are distances between countries measured? 2. Why is odometer included in the dashboard of every vehicle? 3. Why is there a need to have standard units in expressing various measurements like distance and time? 4. How important is it to learn how to read analog clocks? 5. If you are to make your own measuring tool for distance and time, how do you want it to look like? What will be the special feature that makes it different from the usual measuring tools? 22  Lesson 8.3: Calculating Speed and Velocity Objective In this lesson, you should be able to: calculate the speed and/or velocity of an object. Speed and velocity are both descriptors of motion. Speed refers to how fast or slow an object is moving. On the other hand, velocity is known as the speed with a certain direction. But what are the quantities required in order to determine the speed or velocity of a moving object? How do you compute the speed or velocity of a moving object? Warm-Up Kids Car Racers Materials: mobile device (i.e. tablet, smart phones) with an internet connection Procedure: 1. Install the Kids Car Racers mobile application in your device. To do this, connect to the Internet and go to Google Playstore for Android devices and Apple Store for IOS device. Download and install the “Kids Car Racers” (Google Play Store) app. 3583 Bytes. 2018. ‘Kids Car Racers’. https://play.google.com/store/apps/details?id=com.ogien.kidscarracers&hl=en Download and install the “Kids Car Racers” (Apple Store) app. 3583 Bytes. 2018. ‘Kids Car Racers’. https://itunes.apple.com/us/app/kids-car-racers/id816002217?mt=8 23  2. Play the game for 5 minutes. Tilt the device to control the car and collect the coins. 3. Observe the movement of the car as you play the game. Guide Questions: 1. How will you describe the movement of your racing car? 2. What makes the car move slower or faster? 3. Was it easy to control the car’s movement? Why or why not? Learn about It Computing for Speed Speed is defined as the rate of change in the position of a moving object. It tells how fast or slow an object is moving. In describing speed, it is important to determine how much distance is covered by an object over a period of time. A moving object that covers the longer distance in a shorter amount of time is said to be faster. On the contrary, an object is said to be slow if it took a longer time to cover the same amount of distance. Mathematically, the speed of an object is computed using the equation below: where s is the speed in meters per second (m/s), d is the distance in meters (m), and t is time in seconds (s). 24 Speed is always expressed with a unit of distance per unit of time. Some units for speed are kilometer per hour (kph), miles per hour (mph), or meter per second (mps). Fig. 9. The blue car travelled twice faster than the red car. Though both cars covered the same distance, the blue car covered it in a shorter amount of time than the red car. Motorists can instantly determine the speed of their moving vehicles through the speedometer. It is an instrument found on the dashboard of a car that displays how fast the car is moving at a particular time. Fig. 10. A speedometer is an instrument attached on the dashboard of a car. It tells the speed at a particular time of a moving car. 25 Computing for Velocity Velocity refers to the rate of change in the position of a moving object with respect to the frame of reference. The frame of reference is the basis for identifying the direction of a moving object. Instead of dividing the distance by time, the displacement of the object is measured over a certain period of time. It is the reason why velocity is known as the speed with direction. Mathematically, the velocity of an object may be computed using the equation below: where v is velocity in meters per second (m/s), d is displacement in meters (m) and t is time in seconds (s). Similar to speed, velocity is expressed with a unit of distance per unit of time. However, there should always be a direction indicated in every unit of speed. Worked Examples Example 1 Leon walked from his house to the community library. It took him 10 minutes to reach his destination which is 3 meters away from his house. What is Leon’s walking pace as he travels from his house to the community library? Solution Step 1 Identify what is required to find in the problem. You are asked to calculate for the walking pace of Leon. 26 Step 2 Identify the given in the problem. The distance travelled, as well as, time are given in the problem. Step 3 Write the working equation. Step 4 Substitute the given values. Step 5 Find the answer. Therefore, the walking pace of Leon is 0.3 m/min. Let us Practice A woman walks 500 meters in 80 seconds. What is her walking pace? Example 2 An arrow released from a bow travelled 4 meters forward in 2 seconds. What is the velocity of the arrow? Solution Step 1 Identify what is required to find in the problem. You are asked to calculate for the velocity of the arrow. Step 2 Identify the given in the problem. The distance travelled, as well as, time are given in the problem. Step 3 Write the working equation. 27 Step 4 Substitute the given values. Step 5 Find the answer. Therefore, the velocity of the arrow is 2 m/s forward. Let us Practice A bus heading North covered 20 km in 2 hours. What is the bus’ velocity? Example 3 A car has a velocity of 3.5 m/s, East. What is the car’s displacement if it traveled for 30 s? Solution Step 1 Identify what is required to find in the problem. You are asked to find the displacement that the car will cover for 30 s. Step 2 Identify the given in the problem. The velocity of the car and the time it traveled are given in the problem. Step 3 Write the working equation. Step 4 Substitute the given values. Step 5 Find the answer. 28 Therefore, the displacement covered by the car is 105 m East. Let us Practice A car has a velocity of 10 m/s, North. What is the car’s displacement if it traveled for 45 s? Example 4 A car travels at a constant speed of 2 m/s. How far will the car travel in 300 seconds? Solution Step 1 Identify what is required to find in the problem. You are asked to determine the distance that the car will cover for 300 s. Step 2 Identify the given in the problem. The speed of the car and the time it traveled are given in the problem. Step 3 Write the working equation. Step 4 Substitute the given values. Step 5 Find the answer. Therefore, the distance covered by the car is 600 m. Let us Practice A car going North traveled 8 km per hour for 2.5 hours. How far did the car 29 travel? Example 5 An arrow released from a bow travelled 15 meters at a speed of 3 m/s to reach the target. How long will it take for the arrow to reach the target? Solution Step 1 Identify what is required to find in the problem. You are asked to calculate the time it takes for the arrow to reach the target. Step 2 Identify the given in the problem. The speed, as well as, the distance travelled by the arrow are given in the problem. Step 3 Write the working equation. Step 4 Substitute the given values. Step 5 Find the answer. Therefore, the arrow will take 5 seconds to reach the target. Let us Practice The golf ball hit by the player flies in the air for 150 meters with a speed of 2.5 m/s. How long did the golf ball fly with that certain speed? 30 Example 6 Suppose your fastest speed while walking is 5 km/h. How long will you cover for 3 hours in miles? Solution Step 1 Identify what is required to find in the problem. You are asked to determine the distance you will cover in miles. Step 2 Identify the given in the problem. The speed in walking, as well as, the time are given in the problem. Step 3 Write the working equation. Step 4 Substitute the given values. Step 5 Now that you obtained the distance in kilometers, you may convert it to miles. Take note that 1 km = 0.62 miles. Step 6 Find the answer. Therefore, you will cover 9.3 miles in 3 hours of walking. Let us Practice Suppose your speed while walking is 3 km/h. How long will you cover for 4 hours in miles? 31  Key Points Speed is computed by dividing the distance by the duration of its motion. The mathematical equation for speed is: where s is speed in meter per second (m/s), d is distance in meter (m), and t is time in second (s). Velocity is computed by dividing the displacement of the moving object by the duration of its motion. The mathematical equation for velocity is: where v is velocity in meter per second (m/s), d is displacement in meter (m) and t is time in seconds (s). Web Links For further information regarding speed and velocity, you can check the following web links: Watch this video to find out more about the speed of the fastest train in the world. BBC News. 2015. ‘Japan: World’s fastest train 603 km/h - BBC News.’ https://www.youtube.com/watch?v=HpRqlehZ0X8 Read this article to understand more about speed and velocity by designing a model roller coaster. Seratore, Kathy. 2018. ‘Investigating Speed and Velocity.’ https://serc.carleton.edu/sp/mnstep/activities/speedvelocity.html Watch this video to learn more about the differences between speed and velocity of a moving body. ParticleMen. 2009. ‘They Might Be Giants - Speed and Velocity w/ Marty Beller.’ https://www.youtube.com/watch?v=DRb5PSxJerM 32  Check Your Understanding A. Read and analyze the following statements given. Tell whether the statement is true or false. 1. The velocity of an object is its speed with a direction. 2. A fast moving object covers a short distance for a long period of time. 3. The velocity of an object is always expressed in the unit of distance over a unit of time with specific direction. 4. To compute for the distance covered by a moving object, multiply its speed by the time it is travelling. 5. The speed of an object is always expressed in the unit of meters (m). B. Compute for the speed of the following participants in a marathon. Then, rank the runners by writing 1st for the fastest, 2nd for the next, and so on. Runner Distance Time Elapsed Speed Aleck 6 000 m 600 s (1) Brent 6 000 m 800 s (3) Carlisle 6 000 m 750 s (5) Denise 6 000 m 1 500 s (7) Elle 6 000 m 640 s (9) Runner Rank Aleck (2) Brent (4) Carlisle (6) Denise (8) Elle (10) 33  Challenge Yourself Answer the following questions briefly. 1. How does a speedometer work? 2. Without calculating, how will you know that an object moved fast or slow? 3. Why do some objects move at a constant speed? Give a specific example and justify the reason why it moves at a constant speed. 4. Suppose you want to know your walking pace as you transfer from one location to another. However, you do not have a measuring tool to determine your distance. How will you compute for your walking pace then? 5. In what ways do calculating speed and velocity help you as a student? 34  Lesson 8.4: Calculating Acceleration Objective In this lesson, you should be able to: calculate the acceleration of a moving object. Speed is not always constant. There are instances wherein a moving object increases its speed or suddenly stops. When an object speeds up, it is known to be accelerating. However, when an object slows down, it is said to be decelerating. How do you quantify the acceleration or deceleration of an object? Warm-Up Kick Ball Materials: rubber or plastic ball Procedure: 1. Form a circle with six to eight members to play this game. 2. The goal of the game is to change the speed of the ball by kicking it. The challenge is to keep the ball moving by continuously kicking it within the circle you formed. 3. As you play the game, observe the movement of the ball particularly its speed and direction. Guide Questions: 1. How will you describe the movement of the ball as you continuously kick it? 2. What makes the ball move slowly or fast? 3. If you used a heavier ball, how do you think the game will go on? 4. How is acceleration manifested in the game you played? 35  Learn about It The rate of change in the velocity of a moving object over a certain period of time is known as acceleration. Velocity should change for acceleration to occur. Velocity changes when either the speed or direction of the object also changes. If an object is moving at a constant speed, then its acceleration is zero. The same thing occurs when the object moves in a straight line. Fig. 11. A car going around a curve is still accelerating even if its speed remains constant. Acceleration may be positive or negative. If an object at rest starts to move, positive acceleration happens. This is also true to an object moving at a constant speed then suddenly speeds up. Positive acceleration happens to an object that increases its speed. On the other hand, negative acceleration happens when an object slows down or goes on a full stop. For instance, when a biker presses the pedal brake of his bicycle, the bicycle slows down until it comes to a full stop. This shows negative acceleration which is also known as deceleration. Computing for Acceleration In computing for acceleration, it is important to determine the difference between the final velocity and the initial velocity. The initial velocity tells how fast the object is moving towards a certain direction at the start of motion while the final velocity is the velocity of the object after a certain period of time. There are instances when both the initial and final velocities are zero. For example, when a 36 vehicle started from rest, its initial velocity is zero. If the car stopped moving at the end, its final velocity is also zero. Therefore, the acceleration of the said vehicle also amounts to zero. The difference between the final velocity and initial velocity tells the change in velocity of the moving object. Afterwards, divide the change in velocity by the time that the object travelled. where a is the acceleration in meter / second squared (m/s2), vf and vi are the final and initial velocities respectively, which are both in meter / second (m/s) and t is time in seconds (s). The unit for acceleration is the unit used for velocity over time. The most common units for acceleration are meter per second per second (mps/s or m/s/s) which can also be renamed as meter per second squared (m/s2). Other units for acceleration are kilometer per hour squared (km/h2) and miles per hour squared (mi/h2). The acceleration of an object is affected by several factors such as the force applied for an object to move and the mass of the moving object. Force makes an object move. A stronger force can lead to a greater kind of movement. Therefore, the more force applied to an object, the higher its acceleration. However, heavy objects will require a greater amount of force for them to accelerate. If an equal amount of force is applied to two objects with different mass, the lighter object will accelerate faster compared to the heavier one. 37  Worked Examples Example 1 A car at rest starts to move forward with a speed of 2 m/s for 40 s. What is the acceleration of the car? Solution Step 1 Identify what is required to find in the problem. You are asked to determine the acceleration of the car. Step 2 Identify the given in the problem. The car’s initial and final velocities and time are given in the problem. Take note that the initial velocity is 0 since the car started at rest. Step 3 Write the working equation. Step 4 Substitute the given values. Step 5 Find the answer. Therefore, the acceleration of the car is 0.05 m/s2. Let us Practice A ball initially at rest moved forward with a speed of 3.0 m/s, after being kicked. It continued rolling for 20 seconds. What is the ball’s acceleration? 38 Example 2 A rolling ball initially moves forward with a speed of 300 cm/s. When it passed on a slippery surface, its speed increased to 600 cm/s and it continued rolling for 30 s. What is the acceleration of the ball? Solution Step 1 Identify what is required to find in the problem. The problem requires you to determine the acceleration of the rolling ball. Step 2 Identify the given in the problem. The marble’s initial and final velocities, and time are given in the problem. Step 3 Write the working equation. Step 4 Substitute the given values. Step 5 Find the answer. Therefore, the work done to the cart by the applied force is 10 cm/s2. Let us Practice A car which is running at a constant speed of 1 500 km/h slows down to 1 400 km/h for 0.25 h. What is the acceleration of the car? 39 Example 3 A car that is moving 4000 cm/s speeds up to 6000 cm/s in 4 seconds. What is the acceleration of the car in m/s2? Solution Step 1 Identify what is required to find in the problem. You are asked to determine the acceleration of the car in m/s2. Step 2 Identify the given in the problem. The car’s initial velocity, final velocity, and time are given in the problem. Step 3 Write the working equation. Step 4 Since the given velocity is in centimeters per second (cm/s), it should be converted into meters per second (m/s). Take note that 1 m = 100 cm. Step 5 Substitute the given values. Step 5 Find the answer. Therefore, the acceleration of the car is 5 m/s2. 40  Let us Practice A race car that is moving 2500 cm/s speeds up to 7000 cm/s in 5 seconds. What is the acceleration of the race car in m/s2? Key Points Acceleration is computed by dividing the change in velocity by the time that the object travelled. The mathematical equation for acceleration is: where a is the acceleration in meters/second squared (m/s2), vf and vi are the final and initial velocities respectively, which are both in meters/second (m/s) and t is time in seconds (s). The acceleration of an object is affected by several factors such as the force that is applied to an object to move and the mass of the moving object Web Links For further information about acceleration of an object, you can check the following web links: Watch this video to understand more about the acceleration of an object. Don’t Memorise. 2017. ‘Physics - What’s Acceleration?.’ https://www.youtube.com/watch?v=vxFYfumAAlY Try to play this 3D car racing game by changing its acceleration. Y8 Games. 2017. ‘Maximum Acceleration.’ http://www.y8.com/games/maximum_acceleration 41  Check Your Understanding A. Read and analyze the following statements given. Tell whether the statement is true or false. 1. The speed of an object is not always constant especially if it is moving or changing its position. 2. The rate of change in the velocity of a moving object over a certain period of time is known as acceleration. 3. The final velocity tells how fast the moving object is moving towards a certain direction at the start of motion. 4. An object at rest has an initial velocity of zero. 5. The unit for the acceleration of an object is just the same as the unit of its velocity. B. On the box, put a check (✔) if acceleration takes place in the given situation and cross (Χ) if not. ⬜ 1. The top is spinning at a constant speed. ⬜ 2. A car makes a U-turn on the main road. ⬜ 3. The rolling ball suddenly stops as it hits the wall. ⬜ 4. The runner increases his speed as he approaches the finish line. ⬜ 5. The golf ball remains at rest on top of the tree. C. Read and analyze the following situations given. Tell whether the situation shows acceleration or deceleration. 1. a plane taking off from the hangar 2. a runner reaching the finish line 3. a car approaching a red traffic light 4. a wheel rolling on a steep hill 5. a sailboat moving against a strong wind 42  Challenge Yourself Answer the following questions briefly. 1. How does the mass of an object and the force applied to it affect its acceleration? 2. Suppose a ball is rolling at a constant speed. What factors do you think can cause the ball to change its speed? 3. What do you think will happen if an object suddenly accelerates or decelerates? 4. How is the concept of acceleration applied in the rides found in amusement parks? 5. How does understanding the concept of acceleration be beneficial to you as a student? 43  Laboratory Activity Activity 8.1 Fun Run Objectives At the end of this laboratory activity, the students should be able to: measure the distance to be traveled using a meterstick; record the length of time to be traveled using a stopwatch; calculate one’s speed and acceleration when running. Materials meter stick stopwatch chalk Procedure 1. This activity may be done in a gymnasium or an open field where running is possible. 2. On the floor or ground, trace a 10-meter line using a meterstick and a chalk which will serve as your running path. 3. To begin the fun run, start running from one end of the line to the other end. 4. Make sure to ask someone to record the time you finished running from end to end. 5. Run on the 10-meter line for three times. 6. Record the time it took you to cover the 10-meter distance in the table given below. 7. Compute for your speed on the three different runs that you had using the formula for speed. 44 Data and Results Table 1. Running Speed Record Distance Covered Time Elapsed Speed Trial (m) (s) (m/s) 1 100 2 100 3 100 Guide Questions 1. How will you describe your average speed in the three trials? 2. In which trial did you run the fastest? 3. How can you make your speed record into velocity? 4. Since you started at rest, what is your acceleration when you run with a speed in trial 3 for 10 seconds? 5. How important is it to record time accurately when computing for speed? Performance Task Promoting Road Safety Goal Your goal is to promote road safety in your community by creating a slogan-poster that reminds everyone to be safe when travelling. Role Together with a partner, create a catchy slogan-poster that will inform the people of what to do to avoid accidents and injuries while on the road. Include warnings that may remind people to slow down when driving since accidents occur when driving at high speed. Audience Your clients are the motorists, commuters, and pedestrians who are often on the road. 45 Situation Suppose you are in a community where there is a road that is accident prone to vehicles as well as pedestrians. You need to help in preventing or lessening motion-related accidents in that particular road. Product, Performance, and Purpose On a ⅛ illustration board, you and your partner will create a slogan-poster that will remind the motorists, commuters, and pedestrians to observe safety when travelling. The slogan-poster must be catchy and comprehensive. Standards and Criteria Your performance will be graded by the following rubric. Needs Successful Exemplary Below Expectations, Criteria 0% to 49% Improvement Performance Performance 50% to 74% 75% to 99% 100% Content. Details not Details are Details are Details are presented. presented but not presented in an presented in an Details included in Content is not organized. There organized manner. organized matter the slogan are related to the task. are some contents Content is related that can be easily presented well. that are not to the task. understood. Content related to the related to the task. Content is related theme of the task. to the task. Additional supporting details are presented. Creativity and Presentation was Presentation was Presentation was Presentation was not done. done but in a done smoothly but done clearly. Design. disorganized and the concepts are Concepts were Presentation was illogical manner. presented in such presented in a done in a clear and a way that should logical manner logical manner. The be rearranged for and easily design is simple yet better understandable by appealing. understanding. the audience. 46  Self Check After studying this unit, can you now do the following? Check I can… differentiate distance from displacement. differentiate speed from velocity. identify some tools used to measure distance and time. name some standard units in expressing distance and time. measure the distance covered by a moving object over a period of time. compute for speed and velocity. compute for acceleration. Key Words Acceleration This is the rate of change in velocity over a certain period of time. Distance It tells how far two objects are from one another. Displacement It refers to how far an object travelled with respect to a frame of reference. Motion It is a change in the position of an object over time. Speed This refers to the rate of change in the position of a moving object. Time It refers to the duration of a period or how long an object is moving. Velocity It is the rate of change in position of a moving object with respect to a frame of reference. 47  Key Formula Concept Formula Description Speed Use this formula to solve for speed if distance and time are given. where: s is speed in meters per second (m/s) d is distance in meters (m) t is time in seconds (s) Use this formula to solve for distance if speed and time are given. Use this formula to solve for time if speed and distance are given. Velocity Use this formula to solve for velocity if displacement and time where: are given. v is speed in meters per second (m/s) with direction d is displacement in meters (m) with direction t is time in seconds (s) Use this formula to solve for displacement if velocity and time are given. Use this formula to solve for time if velocity and distance are given. 48  Acceleration Use this formula to solve for acceleration if final and initial velocities and where: time are given. a is acceleration in meters per second per second (m/s/s or m/s2) Vf is the final velocity in meters per second (m/s) Vi is the initial velocity in meters per second (m/s) t is time in seconds (s) Wrap Up Motion Descriptors Photo Credits Fig 3. Distance and Displacement by Stannered is licensed under CC BY-SA 3.0 via Wikimedia Commons. 49  References Peters, Joseph M. and Stout, David L. 2011. Science in Elementary Edition, Methods, Concepts, and Inquiries. Boston: Pearson Education, Inc., U.S. Handwerker, Mark J. 2004. Science Essentials Elementary Level. New York: Jossey-Bass Inc., U.S. Gega, Peter C. and Peters, Joseph M. 1998. Concepts and Experiences in Elementary School Science. New Jersey: Prentice Hall, Inc., U.S. 50