Phys Int CC Ch 2 - Motion in a Straight Line - Answers PDF

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CK-12 Physics Concepts - Intermediate Answer Key Chapter 2: Motion in a Straight Line 2.1 Position and Displacement Practice Questions 1. What is position? 2. Can two objects be the same distance from a single point but be in different positions? Why or why not? 3. What is the difference between distance and displacement? 4. Does distance have direction? Does displacement have direction? Answers 1. Position is an object’s location in relation to a reference point. 2. Yes. As in the movie theater example, an object can be one unit positive from the reference point and a different object can be one unit negative from the reference point. Both objects are one unit away (the same distance), but they occupy different locations in space because they are in different directions. 3. Distance is the total amount an object has traveled, while displacement is the shortest distance between the object’s starting and finishing point. 4. Distance does not have direction. Objects can be one unit away from a point in every direction. However, displacement does have a direction. Displacement is defined as a specific distance in a specific direction. Review Questions 1. Explain the difference between distance and displacement in your own words. 2. Suppose that John lives on a square block that is 180 yards per side, and in the evenings, he walks with his dog around the block for a little exercise. a. If John walks once around the block, what distance does he travel? b. If John walks once around the block, what is his final displacement? 3. Joanna’s house is 8000 feet due west of her school. If her house is assigned the position of zero and her school is assigned the position of +8000, what would Joanna’s position be if she walked 100 feet west of her house?

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Answers 1. Distance is the total units traveled by an object as it changes position, while displacement is the net change in position. 2. a. John will have traveled a distance of 720 yards. b. John’s displacement is zero because he ends up exactly where he started – his house. 3. Joanna will be at -100. 2.2 Average Velocity Practice Questions 1. The velocity versus time graph in the video is divided into six sections. In how many of these sections is the velocity constant? 2. In how many sections of the graph is the velocity zero? 3. What does the area under the curve of a velocity versus time graph represent? Answers 1. The velocity is constant in every horizontal section. Therefore, the velocity is constant in 3 sections: from t=4 to t=8, from t=10 to t=14, and from t=16 to t=20. 2. The velocity is zero in one section, from t=10 to t=14. 3. The area under the curve of a velocity versus time graph represents the total distance moved. Review Questions 1. On a one-day vacation, Jane traveled 340 miles in 8.0 hours. What was her average speed? 2. An object on a number line moved from x = 12 m to x = 124 m and moved back to x = 98 m. The time interval for all the motion was 10. s. What was the average velocity of the object? 3. An object on a number line moved from x = 15 cm to x = 165 cm and then moved back to x = 25 cm all in a time of 100 seconds. a. What was the average velocity of the object? b. What was the average speed of the object?

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Answers 1. 340miles / 8 hours = 42.5 mph 2. x1=12 m, x2=98 m: x=86 m; t =10 s. 3. a. b. 2.3 Instantaneous Velocity Practice Questions Draw a velocity versus time graph for an object whose constant velocity is 15 m/s and whose position starts at x=0 when t=0. Graph the motion for the first 5.0 seconds. Use this resource to answer the questions that follow. 1. In the graph on the video, what is graphed on the vertical axis? 2. What is graphed on the horizontal axis? 3. What does the slope of this graph represent? Answers

1. Velocity is graphed on the vertical axis. 3

2. Time is graphed on the horizontal axis. 3. The slope of the graph represents the acceleration. Review Questions

1. For the motion graphed in the position versus time graph shown above, what is the average velocity in the time interval 1 to 3 seconds? 2. For the motion graphed in the position versus time graph shown above, what is the average velocity in the time interval 3 to 4 seconds? 3. For the motion graphed in the position versus time graph shown above, what is the average velocity in the time interval 5 to 6 seconds? Answers 1. x/t = 40m / 2s = 20 m/s. The average velocity from 1 to 3 seconds is 20 m/s. 2. x/t = 0m / 1s = 0 m/s. The average velocity from 3 to 4 seconds is 0 m/s. 3. The position at t=5s must be estimated. 47m is a good approximation, but answers will vary. Assuming 47m gives: x/t = (20-47)m / 1s = -27 m/s. The average velocity from 5 to 6 seconds is -27 m/s. 2.4 Average Acceleration Practice questions are linked on the page; the linked activity has answers there. Review Questions 1. The velocity of a car increases from 2.0 m/s to 16.0 m/s in a time period of 3.5 s. What was the average acceleration? 2. If an automobile slows from 26 m/s to 18 m/s in a period of 4.0 s, what was the average acceleration? 3. If a runner increases his velocity from 0 m/s to 20 m/s in 2.0 s, what was his average acceleration? 4

4. If a runner decreases his velocity from 20 m/s to 10 m/s in 2.0 s, what was his average acceleration? Answers

1. 2. 3. 4. 2.5 Uniform Acceleration Practice Questions Based on the knowledge you already have, fill in these three graphs, assuming an object begins at x = -10m, vi = 0m/s, and a = 0.5m/s2. Let the top graph show position in meters (blue arrow), the middle graph show velocity in meters per second (red arrow), and the bottom graph show acceleration in meters per second squared (green arrow). The labels across the bottom (0 to 20) are time, in seconds.

Download this activity, and use it to answer the questions below about the relationships between position, velocity, and acceleration. http://phet.colorado.edu/en/simulation/moving-man 1. Familiarize yourself with the program. Then, set the initial position to -10m, the velocity to 0 m/s, and the acceleration to 0.5 m/s 2. Run the program, and look at the graphs the program produces. How do they compare to the graphs you predicted? For each graph, explain why it looks as it does. 5

2. Given the velocity and acceleration graphs given here, draw the man's position graph. Assume he starts at 0m.

3. Given the position and velocity graphs given here, draw the acceleration graph. Assume the man starts at 0 m/s2.

Answers 1. The correct graphs look like these:

Beginning with the acceleration graph, we see that the acceleration is constant at 0.5 m/s2 for the duration of the 20 s. The velocity begins at 0 m/s, but has a constant increase throughout the time. If one was to calculate the slope, it would be 0.5 m/s2, which is the same value as the acceleration, as one would expect. The position graph is an increasing curve, with the initial position at -10 m. As the velocity increases, the slope of the position curve increases as well.

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2. The position graph looks like this:

3. The acceleration graph looks like this:

Review Questions 1. If an object has zero acceleration, does that mean it has zero velocity? Give an example. 2. If an object has zero velocity, does that mean it has zero acceleration? Give an example. 3. If the acceleration of a motorboat is 4.0 m/s 2, and the motorboat starts from rest, what is its velocity after 6.0 s? 4. The friction of the water on a boat produces an acceleration of -10. m/s 2. If the boat is traveling at 30. m/s and the motor is shut off, how long it take the boat to slow down to 5.0 m/s? Answers 1. No. An object with zero acceleration is not changing its velocity. However, it can have any velocity. For example, a car travelling at 60 mph on a straight section of the freeway has a consistent velocity of 60 mph, but it has zero acceleration. 2. No. An object can have a velocity of zero but still have an acceleration. For example, take a ball that has been thrown into the air. At the moment the ball has reached its highest location, the ball has zero velocity. Nonetheless, its direction is changing, which means it has a changing (non-zero) acceleration.

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4. 2.6 Displacement During Constant Acceleration Practice Questions Use this resource to answer the questions that follow: https://www.youtube.com/watch? v=d-_eqgj5-K8 1. For the example in the video, what acceleration is used? 2. What time period is used in the example? 3. What does the slope in the graph represent? 4. What does the area under the curve of the line represent? Answers 1. 2. 3. 4.

The acceleration in the video is 1 m/s 2 The time period is 5 seconds. The slope of the acceleration-time graph is the magnitude of the acceleration The area under the acceleration-time graph is the change in velocity.

Review Questions 1. An airplane accelerates with a constant rate of 3.0 m/s 2 starting at a velocity of 21 m/s. If the distance traveled during this acceleration was 535 m, what is the final velocity? 2. An car is brought to rest in a distance of 484 m using a constant acceleration of -8.0 m/s2. What was the velocity of the car when the acceleration first began? 3. An airplane starts from rest and accelerates at a constant 3.00 m/s 2 for 20.0 s. What is its displacement in this time? 4. A driver brings a car to a full stop in 2.0 s. a. If the car was initially traveling at 22 m/s, what was the acceleration? b. How far did the car travel during braking? Answers 1. Using the formula v2 = v02 + 2ax, the final velocity is 60 m/s 2. Using the formula v2 = v02 + 2ax, the initial velocity was 88 m/s 3. Using the formula x = ½ at2, the displacement is 600 m. 8

4. Δv , a = 11 m/s 2 Δt b. Using the formula x = ½ at2, the displacement is 22 m a. Since

a=

2.7 Acceleration Due to Gravity Practice Questions 1. What is the gravitational acceleration given in the video? Why does it differ from that given in this text? 2. Why does the ball travel further in later time intervals than in the earlier ones? Answers 1. The gravitational acceleration given in the video is 9.81 m/s. This is different because of the altitude of the classroom. 2. The ball travels further later because it has a faster velocity. The change in velocity (acceleration) is consistent, but at higher velocities, this change makes the ball get faster and faster. Review Questions 1. A baseball is thrown vertically into the air with a speed of 24.7 m/s. a. How high does it go? b. How long does the round trip up and down require? 2. A salmon jumps up a waterfall 2.4 m high. With what minimum speed did the salmon leave the water below to reach the top? 3. A kangaroo jumps to a vertical height of 2.8 m. How long will it be in the air before returning to earth? Answers

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