# Lesson 2.15: Physical Science Speed, Velocity & Acceleration

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4 There may be some new math ideas and concepts for students. Please make sure they are comfortable with the work requested of them. If needed, have students work in groups. (Unit 2.15 Handout 2) Activity 2 Online Resources: Online Interactive Resources: If students have Internet connection, they should try to use the online virtual car: velocity and acceleration from PBS Learning Media: Students can also view other aspects of motion, velocity, and acceleration with relationship to NFL Football. This has a video that may help grasp the concepts in a different context. Suggested Teacher Readings: GED Testing Service GED Science Item Sample (to get an idea of what the test may be like) Assessment Guide for Educators: A guide to the 2014 assessment content from GED Testing Service: Minnesota is getting ready for the 2014 GED test! website with updated information on the professional development in Minnesota regarding the 2014 GED. ATLAS: ABE Teaching & Learning Advancement System: 2014 GED Classroom: Science: Minnesota s state-wide website for resources for the science module H. Turngren, Minnesota Literacy Council, 2014 p.4 GED Science Curriculum

5 Unit 2.15 Handout 1 (7 total pages) GROUP A (page 1 of 2) Motion Background for all groups: Relative Motion, Speed, Velocity and Acceleration Groups will present information about relative motion, speed, velocity, and acceleration. Take notes on the page provided about each area in order to gain a better understanding of each concept in physical science. An object is in motion when it is continuously changing its position relative to a reference point and as observed by a person or detection device. For example, you can see that an automobile is moving with respect to the ground. The distance the object goes in a period of time is its speed. If the speed of an object is in a specific direction, it is called velocity. The change in velocity over a period of time is the acceleration of the object. Some questions you will need to answer at the end of the group presentations are: Why must motion be with respect to the observer? What is the difference between speed and velocity? Where is acceleration used? This lesson will answer those questions. Motion All motion is relative to the observer or to some fixed object. Motion can be described as a measure of the distance an object moves in a certain length of time. Example with bus and car For example, when you see a bus drive by, it is moving with respect to you. However, if you are in a car that is moving in the same direction, the bus will be moving at a different velocity with respect to you. If your car is moving in the same direction and same speed as the bus, the bus will appear to not move with respect to you. Of course, if you compare the speed with the ground, both of you will be moving at some velocity. H. Turngren, Minnesota Literacy Council, 2014 p.5 GED Science Curriculum

6 GROUP A (page 2 of 2) Motion Suppose you saw a person walking to the front of the moving bus. The person would be moving faster than the bus from your viewpoint. However, the person would not notice the speed of the bus while he walks to the front. Point of reference In talking about motion, it is important to indicate your point of reference. In the case of moving automobiles, it is usually assumed the speed is with respect to the ground. But there are situations where the speed or velocity may be with respect to another object or an observer. For example, suppose a car was traveling at 60 miles per hour (mph) and hit another car, but there was hardly a dent. The reason could be that the second car was traveling in the same direction at 59 mph, so the car was going only 1 mph with respect to the second car when it hit it. Sun looks like it is moving in the sky Another example of relative motion is how the sun appears to move across the sky, when the earth is actually spinning and causing that apparent motion. Usually, we consider motion with respect to the ground or the Earth. Within the Universe there is no real fixed point. The basis for Einstein's Theory of Relativity is that all motion is relative to what you define as a fixed point. Notes: H. Turngren, Minnesota Literacy Council, 2014 p.6 GED Science Curriculum

7 GROUP B (page 1 of 2) Speed and Velocity Background for all groups: Relative Motion, Speed, Velocity and Acceleration Groups will present information about relative motion, speed, velocity, and acceleration. Take notes on the page provided about each area in order to gain a better understanding of each concept in physical science. An object is in motion when it is continuously changing its position relative to a reference point and as observed by a person or detection device. For example, you can see that an automobile is moving with respect to the ground. The distance the object goes in a period of time is its speed. If the speed of an object is in a specific direction, it is called velocity. The change in velocity over a period of time is the acceleration of the object. Some questions you will need to answer at the end of the group presentations are: Why must motion be with respect to the observer? What is the difference between speed and velocity? Where is acceleration used? This lesson will answer those questions. Speed and Velocity Speed is how fast an object is going with respect to an object. Velocity is a measure of the speed in a given direction. An object s velocity can be constant or changing. An object might move without changing its speed or its direction. That object s velocity is constant. Velocity changes when an object changes speed, or direction, or both. You can say the top speed of an airplane is 300 kilometers per hour (kph). But its velocity is 300 kph in a northeast direction. We distinguish between speed and velocity because if you add the speeds of objects, their directions are important. For example, the velocity of an airplane with respect to the ground would vary according to the direction of the wind. H. Turngren, Minnesota Literacy Council, 2014 p.7 GED Science Curriculum

8 GROUP B (page 2 of 2) Speed and Velocity Measurement To measure speed you use units of length and time. These are measure such as kilometers per hour (km/h) or miles per hour (mi/h). The speed of a moving object may changes. Think of a jogger out on a morning run. The jogger s speed changes during his run. He runs faster on a level or flat path than he does when he runs uphill. He runs fastest downhill. When he stops, time continues to pass, but he is not moving. His speed is zero. Average speed is the total distance traveled dived by the total time it takes to go that distance. You can use a formula to figure average speed. You probably have used the formula in the past. For GED Science 2014 purposes, the formula to remember is: Speed = distance time For example, if a car went 120 miles in 2 hours, its average speed would be the distance of 120 miles divided by the time of 2 hours equaling 60 miles per hour (mph): 60 = You can use a variation of the formula to calculate time. (time = distance speed) If you travel from Milwaukee to Chicago (90 miles) at an average velocity of 60 mph, it would take you 90 mi. 60 mph = 1.5 hours to travel the distance. A different way to use the formula is to calculate the distance, distance = time x speed. If you travel from Minneapolis to Chicago at 65 mph for 7 hours, you can calculate the distance traveled. 65 x 7 = 455 Notes: H. Turngren, Minnesota Literacy Council, 2014 p.8 GED Science Curriculum

9 GROUP C (page 1 of 2) Acceleration Relative Motion, Speed, Velocity and Acceleration Groups will present information about relative motion, speed, velocity, and acceleration. Take notes on the page provided about each area in order to gain a better understanding of each concept in physical science. An object is in motion when it is continuously changing its position relative to a reference point and as observed by a person or detection device. For example, you can see that an automobile is moving with respect to the ground. The distance the object goes in a period of time is its speed. If the speed of an object is in a specific direction, it is called velocity. The change in velocity over a period of time is the acceleration of the object. Some questions you will need to answer at the end of the group presentations are: Why must motion be with respect to the observer? What is the difference between speed and velocity? Where is acceleration used? This lesson will answer those questions. Acceleration Acceleration happens when speed, or direction, or both change. Acceleration is the increase of velocity over a period of time, but it can also be a change in direction. Speeding up is acceleration and slowing down is deceleration. When you start running or jogging, you accelerate (increase your velocity) until you reach a constant speed. A small acceleration tells you that the velocity is changing slowly. A large acceleration tells you that the velocity is changing quickly. Measurement To measure acceleration, you use units of velocity (v) and time (t) in a formula. However, you have to know both the ending and beginning velocities for the formula. Suppose the velocity of a car increased from 50 km/h to 80 km h in 5 seconds as it gets on the highway. What is the average acceleration of the car? H. Turngren, Minnesota Literacy Council, 2014 p.9 GED Science Curriculum

10 GROUP C (page 2 of 2) Acceleration First find the change in velocity. The change in velocity is the difference between the ending velocity (v2) and the beginning velocity (v1). Then divide this difference by the time (t) that had passed. Below is the formula for acceleration: where : a = (v2 v1)/(t) v2 v1 is the end velocity minus the beginning velocity t is the measured time period between the two velocities a (acceleration) = (v2 (80 km/h) v1 (50km.h) ) / (t (5 sec) ) or: 6 km per second = 30 5 Often this formula is written as a = Δv/Δt, where Δ is the Greek letter delta and stands for difference. Another example is if an object speeds up from a velocity of 240 meters/second to 560 meters/second in a time period of 10 seconds, the acceleration is: a = (v2 v1)/(t) a = (v2 = v1 = 240) / t 10 = = = 32 m/s Notes: H. Turngren, Minnesota Literacy Council, 2014 p.10 GED Science Curriculum

11 All Groups (page 1 of 1) Relative Motion, Speed, Velocity and Acceleration Write notes from the group presentations from each area in the space below. Motion: Speed & Velocity: Acceleration: Summary Motion is change in position. All motion is relative to some fixed point or object. Speed is a measurement of that change in position over time. Velocity is speed in a given direction. Acceleration is the increase in speed or velocity over a period of time. Deceleration is the decrease of speed or velocity over time. Information used with permission from: by Ron Kurtus (revised 28 October 2007) H. Turngren, Minnesota Literacy Council, 2014 p.11 GED Science Curriculum

12 Unit 2.15 Handout 2 (4 pages total) Problem Solving Solve the following problems. To solve each, write the equation that will be used. Work out the problem by replacing the words in the equation with the number values from the word problem. Finish by solving for the answer. Be sure to give answer with correct units. Average Speed Use the following equation to calculate speed, you may have to modify the equation to solve problems. Average Speed = Total Distance Total Time Examples: 1. A plane travels 1000 miles in 5 hours. What is the plane s average speed? s=d/t s=1000 miles/ 5hours 200 miles per hour 2. A plane travels 550 miles/hour in 4 hours. How far did the plane travel? d=s x t d=550 miles/hour x 4 hours 2200 miles 3. A girl on a bicycle rides down a hill 500 meters long in 50 seconds. What is the girl s speed? 4. A car moving at a uniform speed travels 32 miles in 0.5 hours. What is the speed of the car? Express your answer in miles per hour. 5. If a marathon runner runs an average speed of 11 miles/hour for three hours. How far did the runner run in in the three hours? H. Turngren, Minnesota Literacy Council, 2014 p.12 GED Science Curriculum

13 Velocity Velocity is the speed of an object in a particular direction. Velocity changes as speed or direction changes. Below calculate velocity. Be sure to include the final direction traveled. Example: 6. A plane travels 500 miles east and lands in Arizona. Then the plane travels another 500 miles east and lands in California. The entire trip was completed in 5 hours. What is the average velocity of the plane? velocity=distance/time v=500mi +500mi 200 miles/hour east 5 7. A girl on a bicycle rides down a hill 600 meters. Then the girl rides up the hill 100 meters and falls off her bicycle. The entire bicycle trip lasted 50 seconds. What is the average velocity of the girl? Acceleration Use the following equation to calculate acceleration and include a reference direction (direction traveled). Acceleration = Example: final velocity starting velocity time it takes to change velocity 8. A runner accelerates from a velocity of 5 miles/hour east until reaching a velocity of 10 miles/hour east in 20 seconds. What was the runner s acceleration? Use above equation. a=10 mi/hr 5 mi/hr.25 mi/hr/s east 20s H. Turngren, Minnesota Literacy Council, 2014 p.13 GED Science Curriculum

14 9. A car traveling at 45 km/hr south passes another car accelerating to 60 km/hr south in 5 seconds. What was the car s acceleration? 10. At point A, a runner is jogging at 3 m/s. Forty seconds later; at point B, the jogger s velocity is only 1 m/s. What is the jogger s acceleration from point A to point B? (note: jogger is decelerating) Extra work: 11. Write your speed problem below and have a classmate solve it. 12. Write your distance problem below and have a classmate solve it. H. Turngren, Minnesota Literacy Council, 2014 p.14 GED Science Curriculum

15 H. Turngren, Minnesota Literacy Council, 2014 p.15 GED Science Curriculum

16 Unit 2.15 Handout 2 Examples: Teacher Answer Key 1. A plane travels 1000 miles in 5 hours. What is the plane s average speed? s=d/t s=1000 miles/ 5hours 200 miles per hour 2. A plane travels 550 miles/hour in 4 hours. How far did the plane travel? d=s x t d=550 miles/hour x 4 hours 2200 miles 3. A girl on a bicycle rides down a hill 500 meters long in 50 seconds. What is the girl s speed? s=d/t s=500 meters/ 50 seconds 10 meters per second 4. A car moving at a uniform speed travels 32 miles in 0.5 hours. What is the speed of the car? Express your answer in miles per hour. s=d/t s=32 miles/.5 seconds 16 miles per hour 5. If a marathon runner runs an average speed of 11 miles/hour for three hours. How far did the runner run in in the three hours? d=s x t d=11 miles/hour x 3 hours 33 miles H. Turngren, Minnesota Literacy Council, 2014 p.16 GED Science Curriculum

17 Velocity Velocity is the speed of an object in a particular direction. Velocity changes as speed or direction changes. Below calculate velocity. Be sure to include the final direction traveled. Example: 6. A plane travels 500 miles east and lands in Arizona. Then the plane travels another 500 miles east and lands in California. The entire trip was completed in 5 hours. What is the average velocity of the plane? Velocity = distance/time v=500mi +500mi 200 miles/hour east 5 7. A girl on a bicycle rides down a hill 600 meters. Then the girl rides up the hill 100 meters and falls off her bicycle. The entire bicycle trip lasted 50 seconds. What is the average velocity of the girl? Velocity = distance/time v=600m-100m 10 m/s down Acceleration 50 s Use the following equation to calculate acceleration and include a reference direction (direction traveled). Acceleration = Example: final velocity starting velocity time it takes to change velocity 8. A runner accelerates from a velocity of 5 miles/hour east until reaching a velocity of 10 miles/hour east in 20 seconds. What was the runner s acceleration? Use above equation. a=10 mi/hr 5 mi/hr.25 mi/hr/s east 20s H. Turngren, Minnesota Literacy Council, 2014 p.17 GED Science Curriculum

18 9. A car traveling at 45 km/hr south passes another car accelerating to 60 km/hr south in 5 seconds. What was the car s acceleration? Use above equation. a= 60km/hr 45 km/hr 3km/hr/s south 5 s 10. At point A, a runner is jogging at 3 m/s. Forty seconds later; at point B, the jogger s velocity is only 1 m/s. What is the jogger s acceleration from point A to point B? (note: jogger is decelerating) Use above equation. a= 1m/s 3 m/s -0.5 m/s/s 40s (any direction) The jogger is decelerating so the answer is negative. Page kilometers per hour kilometers per hour miles per hour miles per hour kilometers per hour miles per hour kilometers per hour miles per hour H. Turngren, Minnesota Literacy Council, 2014 p.18 GED Science Curriculum

19 Unit 2.15 Handout 3 (3 pages total) Name: H. Turngren, Minnesota Literacy Council, 2014 p.19 GED Science Curriculum

20 H. Turngren, Minnesota Literacy Council, 2014 p.20 GED Science Curriculum

21 H. Turngren, Minnesota Literacy Council, 2014 p.21 GED Science Curriculum

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