# Lesson one. Linear Motion. Terminal Objective. Lesson 1. Linear Motion

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1 Lesson one Terminal Objective Using their class notes to complete the handout on linear motion, students will be able to demonstrate their understanding of speed and acceleration by problem solving different scenarios regarding cargo ship movement within the Port of Long Beach. CA Science Content Standards: Physics (introductory level): Motion and Forces 1.a Solve problems that involve constant speed and average speed. Note: Acceleration is also introduced descriptively, without addressing the unbalanced force causing it. Materials Map transparency Ruler Overhead projector Time Required 1 class 1

2 Introduction of Lesson Anticipatory Set Ask the following questions: 1) Define speed in your own words. 2) What do you think of when you hear the word acceleration? 3) What do you think acceleration means? 4) When you drive down Ocean Boulevard and out past the breakwater, you can see cargo ships going to the Port of Long Beach. How fast do you think the ships are traveling? How fast do you think they could speed up? How fast do you think they could slow down? Lesson Input Before we can answer questions about motion, we need to have the tools to solve problems. In this case, we ll need a math tool. Fortunately, what we need is one of the easiest tools: multiplying fractions. Remember how to do this? X = First cancel diagonally. Then, multiply straight across: top x top, bottom x bottom. You can do this with symbols, too. Try this one: AB X C = C DA If you got B/D, you ve mastered what you need to for this lesson. 2

3 Lesson cont d Now you will apply this to rearranging the linear motion equations. For instance, the equation for velocity is, v = d/t which is fine if you want to know what the velocity is. But what if you want to solve for something else, like time? That s when you need to use fraction math. Lesson 1 If the question asks, How long will it take to...?, you are solving for time (t). v = d t When what you want is on the bottom, multiply to get it on top. Just remember to do the same thing on both sides of the = sign. t x v = d t x t t x v = d This would be fine if we wanted to solve for distance. But we want time, so we have to get it alone. 1 v x t x v = d x 1 v Get rid of the v by multiplying by 1/v. t = d v Now we can just plug in d and v. Learning this kind of math can get you through most of chemistry and physics. It takes a lot of mystery out of those scary looking equations! 3

4 Modeling On an overhead projector or document camera, show students how to measure the map distances using a ruler or just the edge of a piece of paper. You may also need to model converting meters to kilometers, and review the units for acceleration, km/hr2. Practice Problems Have students complete the handout Linear Motion. Closure Write down three things you learned regarding speed and acceleration. How are speed and acceleration related? 4

5 Map of the Port of Long Beach Lesson 1 100m 400m Cargo Ship Path Pacific Ocean 5

6 KEY Map of the Port of Long Beach 10,000m 400m 1500m 700m 200m 800m 700m 400m 1200m 400m 700m 500m 100m 400m Cargo Ship Path Pacific Ocean 6

7 Worksheet Lesson one Student Worksheet Background Long Beach, California has the second busiest port in the United States and the 15th busiest container cargo port in the world. With 3,200 acres of land and 80 berths spaced out on 10 piers, it averaged 19, foot cargo containers moved on and off ships each day in The Port of Long Beach s top imports include petroleum, electronics, and plastics from all over the world. In addition, it exports waste paper, chemicals and scrap metals to other countries. Movement within the Port is very busy and requires strict guidelines of cargo ships to ensure the safety of everyone. Definitions: Speed: Velocity: Acceleration: 7

8 Equations distance traveled average velocity = time to travel the distance Questions Use the scale distances on the map to measure and label the dotted line segments showing where ships travel in the Port of Long Beach. Round the distances to the nearest hundred meters. Then, use those distances to solve the following problems. 1. A cargo ship transporting cars from Japan is traveling at a rate of 3.2 km/h as it approaches the Port from the Pacific Ocean (at the point indicated by a star at the bottom of the map). At this rate, how long will it take the ship to reach the berth on Pier J to unload its cargo? 2. Pier T is under development and is in need of large equipment that must be transported from Pier J through boat. It takes the boat 25 minutes to reach Pier T. What is its average speed in km/h? 8

9 Questions cont d 3. A cargo ship leaves Pier F and travels to Pier C to load waste paper to be exported to China. As it turns northwest towards inner harbor it begins to decelerate at a rate of 133 km/h2 for the last 400 m before docking at the berth 5 minutes later. How fast was the ship traveling before slowing down in km/h? Lesson 1 4. Petroleum is exported from Pier A and will be traveling to Mexico. It takes the ship 1.5 hours to reach the Pacific Ocean, where it reaches a top speed of 30 km/h. What was the ship s average acceleration? 5. _If a cargo ship were to enter the middle harbor at 15 km/h and begin slowing down at a rate of 60 km/h2 in order to dock at Pier F, can the ship come to a stop in 10 minutes? 6. A cargo ship is heading from Pier F to Pier E at an average rate of 2.8 km/h. At this rate, how long will it take for the ship to reach the pier in minutes? 7. If the captain slows down at a rate of 5.6 km/h2, will he come to a complete stop in time? 9

10

11 Worksheet KEY Lesson one Lesson 1 Student Worksheet Background Long Beach, California has the second busiest port in the United States and the 15th busiest container cargo port in the world. With 3,200 acres of land and 80 berths spaced out on 10 piers, it averaged 19, foot cargo containers moved on and off ships each day in The Port of Long Beach s top imports include petroleum, electronics, and plastics from all over the world. In addition, it exports waste paper, chemicals and scrap metals to other countries. Movement within the Port is very busy and requires strict guidelines of cargo ships to ensure the safety of everyone. Definitions: Speed: the distance traveled in a given time Velocity: the distance traveled in a given time with direction indicated Acceleration: how fast velocity changes 11

12 Equations distance traveled average velocity = time to travel the distance Questions Use the scale distances on the map to measure and label the dotted line segments showing where ships travel in the Port of Long Beach. Round the distances to the nearest hundred meters. Then, use those distances to solve the following problems. 1. A cargo ship transporting cars from Japan is traveling at a rate of 3.2 km/h as it approaches the Port from the Pacific Ocean (at the point indicated by a star at the bottom of the map). At this rate, how long will it take the ship to reach the berth on Pier J to unload its cargo? Answer: 0.5 hour 2. Pier T is under development and is in need of large equipment that must be transported from Pier J through boat. It takes the boat 25 minutes to reach Pier T. What is its average speed in km/h? Answer: 7.0 km/hour 12

13 Questions cont d 3. A cargo ship leaves Pier F and travels to Pier C to load waste paper to be exported to China. As it turns northwest towards inner harbor it begins to decelerate at a rate of 133 km/h2 for the last 400 m before docking at the berth 5 minutes later. How fast was the ship traveling before slowing down in km/h? Answer: 11.1 km/hour Lesson 1 4. _Petroleum is exported from Pier A and will be traveling to Mexico. It takes the ship 1.5 hours to reach the Pacific Ocean, where it reaches a top speed of 30 km/h. What was the ship s average acceleration? Answer: 45 km/hour 2 5. _If a cargo ship were to enter the middle harbor at 15 km/h and begin slowing down at a rate of 60 km/h2 in order to dock at Pier F, can the ship come to a stop in 10 minutes? Answer: No, it will take 0.25 hour, or 15 minutes, to stop. 6. _ A cargo ship is heading from Pier F to Pier E at an average rate of 2.8 km/h. At this rate, how long will it take for the ship to reach the pier in minutes? Answer: 15 minutes 7. If the captain slows down at a rate of 5.6 km/h2, will he come to a complete stop in time? Answer: No, he will crash into the pier! 13

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