Chapter 2: Motion in One Dimension

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1 Assumption College English Program Mr. Stephen Dobosh s EP- M 4 P h y s i c s C l a s s w o r k / H o m e w o r k P a c k e t Chapter 2: Motion in One Dimension Section 1: Displacement and Velocity Section 2: Acceleration Section 3: Falling Objects Student s Name.... EP-M./. ID #.. Register # Much of the material within this packet is drawn from the course textbook Holt Physics that each of you have purchased. This content is copyrighted 2012 by Holt McDougal, a division of Houghton Mifflin Harcourt Publishing Company. No part of this work may be reproduced or transmitted in any form without prior written permission of the copyright owner.

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5 Mr. Stephen Dobosh Page 5 of 32 Chapter 2.1: Displacement and Velocity (pp ) Practice A, p. 40 #1-6 Due: 1. Heather and Matthew walk with an average velocity of 0.98 m/s eastward. If it takes them 34 min to walk to the store, what is their displacement? 2. If Joe rides his bicycle in a straight line for 15 min with an average velocity of 12.5 km/h south, how far has he ridden? 3. It takes you 9.5 min to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance. What is your displacement? 4. Simpson drives his car with an average velocity of 48.0 km/h to the east. How long will it take him to drive 144 km on a straight highway? 5. Look back at item 4. How much time would Simpson save by increasing his average velocity to 56.0 km/h to the east? 6. A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south. The bus stops for 24 min. Then it travels 210 km south with an average velocity of 75 km/h to the south. a. How long does the total trip last? b. What is the average velocity for the total trip?

6 Mr. Stephen Dobosh Page 6 of 32 Chapter 2.1: Displacement and Velocity (pp ) Formative Assessment 2.1, p. 43 #1-6 Due: 1. What is the shortest possible time in which a bacterium could travel a distance of 8.4 cm across a Petri dish at a constant speed of 3.5 mm/s? 2. A child is pushing a shopping cart at a speed of 1.5 m/s. How long will it take this child to push the cart down an aisle with a length of 9.3 m? 3. An athlete swims from the north end to the south end of a 50.0 m pool in 20.0 s and makes the return trip to the starting position in 22.0s. a. What is the average velocity for the first half of the swim? b. What is the average velocity for the second half of the swim? c. What is the average velocity for the roundtrip? 4. Two students walk in the same direction along a straight path, at a constant speed one at 0.90 m/s and the other at 1.90 m/s. a. Assuming that they start at the same point and the same time, how much sooner does the faster student arrive at a destination 780 m away? b. How far would the students have to walk so that the faster student arrives 5.50 min before the slower student?

9 (2009 ed., Figure 8) shows position-time graphs of the straight-line movement of two brown bears in a wildlife preserve.

7 Mr. Stephen Dobosh Page 7 of Does knowing the distance between two objects give you enough information to locate the objects? Explain. 6. Figure 1.9 (2009 ed., Figure 8) shows position-time graphs of the straight-line movement of two brown bears in a wildlife preserve. a. Which bear has the greater average velocity over the entire period? b. Which bear has the greater velocity at t = 8.0 min? c. Is the velocity of bear A always positive? d. Is the velocity of bear B ever negative?

8 Mr. Stephen Dobosh Page 8 of 32 Chapter 2.2: Acceleration (pp ) Practice B, p. 45 #1-5 Due: 1. As the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at 4.1 m/s 2 as it slows from 9.0 m/s to 0.0 m/s. Find the time interval of acceleration for the bus. 2. A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s 2 to reach a speed of 12.0 m/s. How long does it take for this acceleration to occur? 3. With an average acceleration of 1.2 m/s 2, how long will it take a cyclist to bring a bicycle with an initial speed of 6.5 m/s to a complete stop? 4. Turner s treadmill runs with a velocity of 1.2 m/s and speeds up at regular intervals during a half-hour workout. After 25 min, the treadmill has a velocity of 6.5 m/s. What is the average acceleration of the treadmill during this period? 5. Suppose a treadmill has an average acceleration of m/s 2. a. How much does its speed change after 5.0 min? b. If the treadmill s initial speed is 1.7 m/s, what will its final speed be?

9 Mr. Stephen Dobosh Page 9 of 32 Chapter 2.2: Acceleration (pp ) Practice C, p. 49 #1-4 Due: 1. A car accelerates uniformly from rest to a speed of 6.6 m/s in 6.5 s. Find the distance the car travels during this time. 2. When Maggie applies the brakes of her car, the car slows uniformly from 15.0 m/s to 0.0 m/s in 2.50 s. How many meters before a stop sign must she apply her brakes in order to stop at the sign? 3. A driver in a car traveling at a speed of 21.8 m/s sees a cat 101 m away on the road. How long will it take for the car to accelerate uniformly to a stop in exactly 99 m? 4. A car enters the freeway with a speed of 6.4 m/s and accelerates uniformly for 3.2 km in 3.5 min. How fast (in m/s) is the car moving after this time?

10 Mr. Stephen Dobosh Page 10 of 32 Chapter 2.2: Acceleration (pp ) Practice D, p. 51 #1-4 Due: Note: Each question has two parts! So you need to have two answers for each! 1. A car with an initial speed of 6.5 m/s accelerates at a uniform rate of 0.92 m/s 2 for 3.6 s. Find the final speed and the displacement of the car during this time. 2. An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.00 m/s 2. Find the final speed and the displacement after 5.00 s. 3. A car starts from rest and travels for 5.0 s with a constant acceleration of 1.5 m/s 2.What is the final velocity of the car? How far does the car travel in this time interval? 4. A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of 2.0 m/s 2. How long does it take the car to accelerate to a final speed of 10.0 m/s? How far has the car moved during the braking period?

11 Mr. Stephen Dobosh Page 11 of 32 Chapter 2.2: Acceleration (pp ) Practice E, pp #1-6 Due: 1. Find the velocity after the stroller in Sample Problem E has traveled 6.32 m. 2. A car traveling initially at +7.0 m/s accelerates uniformly at the rate of m/s 2 for a distance of 245 m. a. What is its velocity at the end of the acceleration? b. What is its velocity after it accelerates for 125 m? c. What is its velocity after it accelerates for 67 m? 3. A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s 2. a. What is the speed of the car after it has traveled 55 m? b. How long does it take the car to travel 55 m? 4. A motorboat accelerates uniformly from a velocity of 6.5 m/s to the west to a velocity of 1.5 m/s to the west. If its acceleration was 2.7 m/s 2 to the east, how far did it travel during the acceleration?

12 Mr. Stephen Dobosh Page 12 of An aircraft has a liftoff speed of 33 m/s. What minimum constant acceleration does this require if the aircraft is to be airborne after a take-off run of 240 m? 6. A certain car is capable of accelerating at a uniform rate of 0.85 m/s 2. What is the magnitude of the car s displacement as it accelerates uniformly from a speed of 83 km/h to one of 94 km/h?

13 Mr. Stephen Dobosh Page 13 of 32 Chapter 2.2: Acceleration (pp ) Formative Assessment 2.2, p. 55 #1-6 Due: 1. Marissa s car accelerates uniformly at a rate of m/s 2. How long does it take for Marissa s car to accelerate from a speed of 24.6 m/s to a speed of 26.8 m/s? 2. A bowling ball with a negative initial velocity slows down as it rolls down the lane toward the pins. Is the bowling ball s acceleration positive or negative as it rolls toward the pins? 3. Nathan accelerates his skateboard uniformly along a straight path from rest to 12.5 m/s in 2.5 s. a. What is Nathan s acceleration? b. What is Nathan s displacement during this time interval? c. What is Nathan s average velocity during this time interval? 4. Critical Thinking Two cars are moving in the same direction in parallel lanes along a highway. At some instant, the instantaneous velocity of car A exceeds the instantaneous velocity of car B. Does this mean that car A s acceleration is greater than car B s? Explain, and use examples.

Mr. Stephen Dobosh Page 14 of 32 5. Interpreting Graphics The velocity-versus-time graph for a shuttle bus moving along a straight path is shown in Figure 2.7 (2009 ed., Figure 13). a. Identify the time intervals during which the velocity of the shuttle bus is constant.

14 Mr. Stephen Dobosh Page 14 of Interpreting Graphics The velocity-versus-time graph for a shuttle bus moving along a straight path is shown in Figure 2.7 (2009 ed., Figure 13). a. Identify the time intervals during which the velocity of the shuttle bus is constant. b. Identify the time intervals during which the acceleration of the shuttle bus is constant. c. Find the value for the average velocity of the shuttle bus during each time interval identified in b. d. Find the acceleration of the shuttle bus during each time interval identified in b. e. Identify the times at which the velocity of the shuttle bus is zero. f. Identify the times at which the acceleration of the shuttle bus is zero. g. Explain what the slope of the graph reveals about the acceleration in each time interval. 6. Is the shuttle bus in item 5 always moving in the same direction? Explain, and refer to the time intervals shown on the graph.

15 Mr. Stephen Dobosh Page 15 of 32 Chapter 2.3: Falling Objects (pp ) Practice F, pp #1-4 Due: 1. A robot probe drops a camera off the rim of a 239 m high cliff on Mars, where the free-fall acceleration is 3.7 m/s 2. a. Find the velocity with which the camera hits the ground. b. Find the time required for it to hit the ground. 2. A flowerpot falls from a windowsill 25.0 m above the sidewalk. a. How fast is the flowerpot moving when it strikes the ground? b. How much time does a passerby on the sidewalk below have to move out of the way before the flowerpot hits the ground? 3. A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s. a. What will the ball s speed be when it returns to its starting point? b. How long will the ball take to reach its starting point? 4. Calculate the displacement of the volleyball in Sample Problem F when the volleyball s final velocity is 1.1 m/s upward.

16 Mr. Stephen Dobosh Page 16 of 32 Chapter 2.3: Falling Objects (pp ) Formative Assessment 2.3, p. 61 #1-6 Due: 1. A coin is tossed vertically upward. a. What happens to its velocity while it is in the air? b. Does its acceleration increase, decrease, or remain constant while it is in the air? 2. A pebble is dropped down a well and hits the water 1.5 s later. Using the equations for motion with constant acceleration, determine the distance from the edge of the well to the water s surface. 3. A ball is thrown vertically upward. What are its velocity and acceleration when it reaches its maximum altitude? What is its acceleration just before it hits the ground? 4. Two children are bouncing small rubber balls. One child simply drops a ball. At the same time, the second child throws a ball downward so that it has an initial speed of 10 m/s. What is the acceleration of each ball while in motion? 5. Critical Thinking A gymnast practices two dismounts from the high bar on the uneven parallel bars. During one dismount, she swings up off the bar with an initial upward velocity of m/s. In the second, she releases from the same height but with an initial downward velocity of 3.0 m/s. What is her acceleration in each case? How do the final velocities of the gymnast as she reaches the ground differ?

Mr. Stephen Dobosh Page 17 of 32 6. Interpreting Graphics Figure 3.4 (2009 ed.

Use the graph to sketch the path of the basketball and to sketch a velocity-time graph of the basketball s motion. a. Is the velocity of the basketball constant?

17 Mr. Stephen Dobosh Page 17 of Interpreting Graphics Figure 3.4 (2009 ed., Figure 17) is a position-time graph of the motion of a basketball thrown straight up. Use the graph to sketch the path of the basketball and to sketch a velocity-time graph of the basketball s motion. a. Is the velocity of the basketball constant? (If so, estimate the acceleration.) b. Is the acceleration of the basketball constant? (If so, estimate the acceleration.) c. What is the initial velocity of the basketball?

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28 Mr. Stephen Dobosh Page 28 of 32 SUPPLEMENTAL A Page 1 of 5 Position-Time and Velocity-Time Graph worksheet Adapted from Modeling Instruction Program 2009 Due: 1. Robin, roller skating down a marked sidewalk, was observed to be at the following positions at the times listed below: a. Plot a position vs. time graph for the skater on the graph provided above. b. How far was Robin from the origin at t = 6 s? c. Write a mathematical model that describes the skater's motion. (Hint: What s the general equation for a line? Adapt that to fit this data!) d. Was his speed constant over the entire interval? How do you know?

29 Mr. Stephen Dobosh Page 29 of 32 SUPPLEMENTAL A Page 2 of 5 Position-Time and Velocity-Time Graph worksheet Adapted from Modeling Instruction Program In a second trial, the timer started her watch a bit sooner. The following data were obtained: a. Plot the position vs. time graph for the skater using the graph provided above. b. How far from the origin was the skater at t = 5 s? How do you know? c. Was the skater s speed constant? If so, what was it? d. In the first trial, the skater was further along at 2 s than he was in the second trial. Does this mean that he was going faster? Explain your answer.

30 Mr. Stephen Dobosh Page 30 of 32 SUPPLEMENTAL A Page 3 of 5 Position-Time and Velocity-Time Graph worksheet Adapted from Modeling Instruction Program Suppose now that our skater was observed in a third trial. The following data were obtained: a. Plot the position vs. time graph for the skater using the graph provided above. b. What do you think is happening during the time interval: t = 4 s to t = 6 s? How do you know? c. What do you think is happening during the time interval: t = 6 s to t = 10 s? How do you know? d. Determine the skater's average velocity from t = 0 s to t = 16 s. (Average velocity is the displacement (final position minus initial position) divided by time elapsed.) e. Determine the skater's average speed from t = 0 s to t = 16 s. (Average speed is the distance traveled along the path (change in odometer reading) divided by time elapsed.) f. List some example situations in which average speed is a better measure of motion than average velocity. g. List some example situations in which average velocity is a better measure of motion than average speed.

31 Mr. Stephen Dobosh Page 31 of 32 SUPPLEMENTAL A Page 4 of 5 Position-Time and Velocity-Time Graph worksheet Adapted from Modeling Instruction Program Rank the following graphs: a. Rank the graphs according to which show the greatest average velocity from the beginning to the end of the motion. (Zero is greater than negative, and ties are possible.) Greatest Least Explain your reasoning for your ranking. (Or instead just show your calculations/work above.) b. Rank the graphs according to which show the greatest average speed from the beginning to the end of the motion. Greatest Least Explain your reasoning for your ranking. (Or instead just show your calculations/work above.)

32 Mr. Stephen Dobosh Page 32 of 32 SUPPLEMENTAL A Page 5 of 5 Position-Time and Velocity-Time Graph worksheet Adapted from Modeling Instruction Program 2009 (Questions 5-7) Draw the velocity vs time graphs for an object whose motion produced the position vs time graphs shown below at left. (The first one has been done for you. ) 8. For many graphs, both the slope of the line and the area between the line and the horizontal axis (a.k.a. the area under the curve ) have physical meanings. a. What does the slope of a position-time graph tell you about the motion of an object? b. Looking at the velocity-time graphs, determine the units for a square of area on the graph. c. What quantity does the area under the velocity-time graph tell you about the motion of an object?

1. Haiwa walks eastward with a speed of 0.98 m/s. If it takes him 34 min to walk to the store, how far has he walked?

Practice 1A Average velocity and displacement 1. Haiwa walks eastward with a speed of 0.98 m/s. If it takes him 34 min to walk to the store, how far has he walked? v avg = 0.98 m/s east t = 34 min x =?