Book cover for Physics

Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

ISBN #9781118486894

10th Edition

2,562 Questions

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Summary
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Key Concepts
Example Problems
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Summary

This chapter introduces the fundamental concepts of kinematics in one dimension (and an introduction to two-dimensional motion). Key ideas include the definitions of displacement, speed, velocity, and acceleration, and the proper use of kinematic equations to solve problems involving constant acceleration. Special attention is given to free-fall motion and the importance of sign conventions and graphical analysis in understanding the motion of objects.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

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Example Problems

Example 1

The space shuttle travels at a speed of about $7.6 \times 10^{3} \mathrm{m} / \mathrm{s}$. The blink of an astronaut"s eye lasts about 110 ms. How many football fields (length $=91.4 \mathrm{m})$ docs the shuttle cover in the blink of an eye?

Example 2

For each of the three pairs of positions listed in the following table, determine the magnitude and direction (positive or negative) of the displacement. $$ \begin{array}{lcc} \hline & \text { Initial position } x_{0} & \text { Final position } x \\ \hline \text { (a) } & +2.0 \mathrm{m} & +6.0 \mathrm{m} \\ \text { (b) } & +6.0 \mathrm{m} & +2.0 \mathrm{m} \\ \text { (c) } & -3.0 \mathrm{m} & +7.0 \mathrm{m} \\ \hline \end{array} $$

Example 3

Due to continental drift, the North American and European continents are drifting apart at an average speed of about $3 \mathrm{cm}$ per year. At this speed, how long (in years) will it take for them to drift apart by another $1500 \mathrm{m}$ (a little less than a mile)?

Example 4

You step onto a hot beach with your bare feet. A nerve impulse, generated in your foot, travels through your nervous system at an average speed of $110 \mathrm{m} / \mathrm{s}$. How much time does it take for the impulse, which travels a distance of $1.8 \mathrm{m},$ to reach your brain?

Example 5

The data in the following table describe the initial and final positions of a moving car. The elapsed time for each of the three pairs of positions listed in the table is 0.50 s. Review the concept of average velocity in Section 2.2 and then determine the average velocity (magnitude and direction) for each of the three pairs. Note that the algebraic sign of your answers will convey the direction. $$ \begin{array}{lcc} \hline & \text { Initial position } x_{0} & \text { Final position } x \\ \hline \text { (a) } & +2.0 \mathrm{m} & +6.0 \mathrm{m} \\ \text { (b) } & +6.0 \mathrm{m} & +2.0 \mathrm{m} \\ \text { (c) } & -3.0 \mathrm{m} & +7.0 \mathrm{m} \\ \hline \end{array} $$
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Step-by-Step Explanations

QUESTION

A speedboat starts with an initial velocity of 16.0 m/s and accelerates at a constant rate of 12.0 m/s\u00b2 for 8.0 seconds. What is its displacement?\nStep-by-step Answer:\nStep 1: Identify the known variables: initial velocity (v\u2080 = 16.0 m/s), acceleration (a = 12.0 m/s\u00b2), and time (t = 8.0 s).\nStep 2: Use the kinematic equation for displacement under constant acceleration: x = v\u2080t + \u00bd a t\u00b2.\nStep 3: Substitute the known values: x = (16.0 m/s)(8.0 s) + \u00bd (12.0 m/s\u00b2)(8.0 s)\u00b2.\nStep 4: Compute the terms: first term = 128.0 m; second term = 0.5 * 12.0 * 64 = 384.0 m.\nStep 5: Add the two terms together: x = 128.0 m + 384.0 m = 512.0 m.\nFinal Answer: The displacement of the speedboat is 512.0 meters.\n\n- Topic: Determining Maximum Height in Free-Fall \nQuestion: A coin is tossed upward with an initial speed of 5.00 m/s. Using g = 9.80 m/s\u00b2, what is the maximum height reached by the coin?\nStep-by-step Answer:\nStep 1: At maximum height, the final velocity (v) is 0 m/s.\nStep 2: Use the kinematic equation: v\u00b2 = v\u2080\u00b2 - 2g y, where y is the height.\nStep 3: Rearrange the equation to solve for y: y = v\u2080\u00b2 / (2g).\nStep 4: Substitute values: y = (5.00 m/s)\u00b2 / (2 * 9.80 m/s\u00b2) = 25 / 19.6 \u2248 1.28 m.\nFinal Answer: The coin reaches a maximum height of approximately 1.28 meters.\n\n"

STEP-BY-STEP ANSWER:

Step 1: Identify the known variables: initial velocity (v\u2080 = 16.0 m/s), acceleration (a = 12.0 m/s\u00b2), and time (t = 8.0 s).\nStep 2: Use the kinematic equation for displacement under constant acceleration: x = v\u2080t + \u00bd a t\u00b2.\nStep 3: Substitute the known values: x = (16.0 m/s)(8.0 s) + \u00bd (12.0 m/s\u00b2)(8.0 s)\u00b2.\nStep 4: Compute the terms: first term = 128.0 m; second term = 0.5 * 12.0 * 64 = 384.0 m.\nStep 5: Add the two terms together: x = 128.0 m + 384.0 m = 512.0 m.\nFinal Answer: The displacement of the speedboat is 512.0 meters.\n\n- Topic: Determining Maximum Height in Free-Fall \nQuestion: A coin is tossed upward with an initial speed of 5.00 m/s. Using g = 9.80 m/s\u00b2, what is the maximum height reached by the coin?\nStep-by-step Answer:\nStep 1: At maximum height, the final velocity (v) is 0 m/s.\nStep 2: Use the kinematic equation: v\u00b2 = v\u2080\u00b2 - 2g y, where y is the height.\nStep 3: Rearrange the equation to solve for y: y = v\u2080\u00b2 / (2g).\nStep 4: Substitute values: y = (5.00 m/s)\u00b2 / (2 * 9.80 m/s\u00b2) = 25 / 19.6 \u2248 1.28 m.\nFinal Answer: The coin reaches a maximum height of approximately 1.28 meters.\n\n"
Final Answer: The displacement of the speedboat is 512.0 meters.\n\n- Topic: Determining Maximum Height in Free-Fall \nQuestion: A coin is tossed upward with an initial speed of 5.00 m/s. Using g = 9.80 m/s\u00b2, what is the maximum height reached by the coin?\nStep-by-step Answer:\nStep 1: At maximum height, the final velocity (v) is 0 m/s.\nStep 2: Use the kinematic equation: v\u00b2 = v\u2080\u00b2 - 2g y, where y is the height.\nStep 3: Rearrange the equation to solve for y: y = v\u2080\u00b2 / (2g).\nStep 4: Substitute values: y = (5.00 m/s)\u00b2 / (2 * 9.80 m/s\u00b2) = 25 / 19.6 \u2248 1.28 m.\nFinal Answer: The coin reaches a maximum height of approximately 1.28 meters.\n\n"

"- Topic: Calculating Displacement Using Kinematic Equations \nQuestion: A speedboat starts with an initial velocity of 16.0 m/s and accelerates at a constant rate of 12.0 m/s\u00b2 for 8.0 seconds. What is its displacement?\nStep-by-step Answer:\nStep 1: Identify the known variables: initial velocity (v\u2080 = 16.0 m/s), acceleration (a = 12.0 m/s\u00b2), and time (t = 8.0 s).\nStep 2: Use the kinematic equation for displacement under constant acceleration: x = v\u2080t + \u00bd a t\u00b2.\nStep 3: Substitute the known values: x = (16.0 m/s)(8.0 s) + \u00bd (12.0 m/s\u00b2)(8.0 s)\u00b2.\nStep 4: Compute the terms: first term = 128.0 m; second term = 0.5 * 12.0 * 64 = 384.0 m.\nStep 5: Add the two terms together: x = 128.0 m + 384.0 m = 512.0 m.\nFinal Answer: The displacement of the speedboat is 512.0 meters.\n\n- Topic: Determining Maximum Height in Free-Fall \nQuestion: A coin is tossed upward with an initial speed of 5.00 m/s. Using g = 9.80 m/s\u00b2, what is the maximum height reached by the coin?\nStep-by-step Answer:\nStep 1: At maximum height, the final velocity (v) is 0 m/s.\nStep 2: Use the kinematic equation: v\u00b2 = v\u2080\u00b2 - 2g y, where y is the height.\nStep 3: Rearrange the equation to solve for y: y = v\u2080\u00b2 / (2g).\nStep 4: Substitute values: y = (5.00 m/s)\u00b2 / (2 * 9.80 m/s\u00b2) = 25 / 19.6 \u2248 1.28 m.\nFinal Answer: The coin reaches a maximum height of approximately 1.28 meters.\n\n"

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Common Mistakes

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