CK-12 Physics FlexBook® 2.0 Answer Key Chapter 2: Motion in One-Dimension 2.1 Position and Displacement 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. 1. If John walks once around the block, what distance does he travel? 2. 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? Answers 1. Distance is the total units traveled by an object as it changes position, while displacement is the net change in position. 2. 1. John will have traveled a distance of 720 yards. 2. John’s displacement is zero because he ends up exactly where he started – his house. 3. Joanna will be at -100. Explore More 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. 2.2 Average Velocity 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? Answers 1. 340miles / 8 hours = 42.5 mph 2. x1 =12 m, x2=98 m: Δx=86 m; Δt =10 s. Δx/Δ t = 86m/10s = 8.6 m/s 3. a. Δx/Δt = 10cm/100s = 0.1 m/s b. Δx/Δt = (165-15cm) + (165-25) / 100s = 290 cm / 100s = 2.9 cm/s Explore More Questions 1. What is the main difference between average speed and average velocity? Answers 1. Average speed is calculated by dividing the total distance travelled by the time interval. Average velocity involves total displacement, instead of distance. 2.3 Instantaneous Velocity Review 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 the graph below to answer the following 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. Δx/Δt = 40m / 2s = 20 m/s. The average velocity from 1 to 3 seconds is 20 m/s. 2. Δx/Δt = 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: Δx/Δt = (20-47)m / 1s = -27 m/s. The average velocity from 5 to 6 seconds is -27 m/s. Explore More Questions Use this resource to answer the questions that follow: https://youtu.be/sujsb5ZlM8o. 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. 2. Time is graphed on the horizontal axis. 3. The slope of the graph represents the acceleration. 2.4 Average Acceleration 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. 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. Δv/Δt = 14m/s / 3.5 s = 4 m/s2 Δv/Δt = -8m/s / 4.0 s = -2 m/s2 2 Δv/Δt = 20m/s / 2.0 s = 10 m/s Δv/Δt = -10m/s / 2.0 s = -5 m/s2 2.5 Uniform Acceleration 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/s2, 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 -10.0 m/s2. If the boat is traveling at 30.0 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. 2 3. Vf = V i+ at = 0 m /s + (4.0 m/s)( 6.0 s) = 24 m/s 2 4. Vf = V i+ at; 5.0 m/s = 30.0 m/s + (-10.0 m/s)(t); t = 2.5 s 2.6 Displacement During Constant Acceleration Review Questions 1. An airplane accelerates with a constant rate of 3.0 m/s2 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/s2 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. 4. a. Since , a = 11 m/s2 b. Using the formula x = ½ at2, the displacement is 22 m Explore More Question Use this resource to answer the questions that follow:https://youtu.be/85SoFmaR9-k 1. What does the area bounded by a velocity versus time graph represent? Answer 1. The area bounded by a velocity versus time graph represents the object’s displacement. 2.7 Acceleration Due to Gravity 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 1. 2 2 2 2 a. a = 9.8 m/s2 ; v / 2a; i=24.7 m/s; v f=0 m/s; v f = v i + 2ad; d= (v f - v i ) 2 2 2 d = (610 - 0 m/s) / 2(9.8 m/s ) = 31 m b. d = 31m; vi=24.7 m/s; vf=0 m/s; d= 1/2(vf - vi)t; t = 2d / (vf + vi); t = 62 m / 24.7 m/s = 2.5 s 2. a = -9.8 m/s2 ; vf=0 m/s; d=2.4m; vf2 = vi2 + 2ad; vi2= vf2 - 2ad; vi2 = 0 m2/s2 - 2(-9.8 m/s2 )(2.4m) = √47 m2/s2 = 6.9 m/s 3. d = 2.8m; 9.8 m/s2 ; d = ½ at2; t= Explore More √ =√ 2d a 2 (2.8m) 9.8m/s2 = 0.76s; 0.76s x 2 = 1.5 s Use this resource to answer the questions that follow: https://youtu.be/izXGpivLvgY. 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. 2.8 Position vs. Time Graphs Review Questions 1. Describe how to make a position-time graph. 2. What is the slope of a line graph? What does the slope of a position-time graph represent? 3. Can a line on a position-time graph have a negative slope, that is, can it slope downward from left to right? Why or why not? 4. In Graph 1 in the Figure above, what is the object’s average velocity? Answers 1. To make a position-time graph, you plot position relative to the starting point on the y-axis against the corresponding time on the x-axis. 2. The slope of a line graph is its steepness. The slope of a position-time graph represents velocity. 3. Yes, a position-time graph can have a negative slope. This would represent the motion of an object that is getting closer to the starting position. 4. The object’s velocity is 10 m/s. 2.9 Velocity vs. Time Graphs Review Questions 1. Describe a velocity-time graph. What does the slope of the graph line represents? 2. In the Figure above, the sprinter reaches a velocity of 2 m/s in just 1 second. At a constant rate of acceleration, how long does it take for her to double this velocity? What is her acceleration during this time period? 3. Create a velocity-time graph by plotting the data in the Table 1.1 below. Answers 1. A velocity-time graph shows how velocity changes over time. It plots velocity on the y-axis and time on the x-axis. Each point on the graph represents the velocity at a given time. The slope of the graph represents acceleration. 2. The runner doubles her velocity to 4 m/s by 2 seconds into the race, so it takes her just 1 second more to reach this velocity. Her acceleration during this period is 2 m/s2 . 3. See sketch of graph below:
