Textbook Question
Every year the Earth travels about 10⁹ km as it orbits the Sun. What is Earth's average speed in km/h?
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Ch. 02 - Describing Motion: Kinematics in One Dimension
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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Table of contents
- Ch. 01 - Introduction, Measurement, Estimating10
- Ch. 02 - Describing Motion: Kinematics in One Dimension30
- Ch. 03 - Kinematics in Two or Three Dimensions; Vectors15
- Ch. 04 - Dynamics: Newton's Laws of Motion16
- Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces22
- Ch. 06 - Gravitation and Newton's Synthesis10
- Ch. 07 - Work and Energy21
- Ch. 08 - Conservation of Energy33
- Ch. 09 - Linear Momentum26
- Ch. 10 - Rotational Motion41
- Ch. 11 - Angular Momentum; General Rotation27
- Ch. 12 - Static Equilibrium; Elasticity and Fracture27
- Ch. 13 - Fluids28
- Ch. 14 - Oscillations14
- Ch. 15 - Wave Motion35
- Ch. 16 - Sound5
- Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law40
- Ch. 18 - Kinetic Theory of Gases18
- Ch. 19 - Heat and the First Law of Thermodynamics31
- Ch. 20 - Second Law of Thermodynamics32
- Ch. 21 - Electric Charge and Electric Field7
- Ch. 23 - Electric Potential20
- Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage15
- Ch. 25 - Electric Current and Resistance32
- Ch. 26 - DC Circuits22
- Ch. 27 - Magnetism21
- Ch. 28 - Sources of Magnetic Field24
- Ch. 29 - Electromagnetic Induction and Faraday's Law21
- Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits42
- Ch. 31 - Maxwell's Equations and Electromagnetic Waves25
- Ch. 32 - Light: Reflection and Refraction42
- Ch. 33 - Lenses and Optical Instruments21
- Ch. 34 - The Wave Nature of Light: Interference and Polarization26
- Ch. 35 - Diffraction24
- Ch. 36 - The Special Theory of Relativity29
- Ch. 38 - Quantum Mechanics1
- Ch. 40 - Molecules and Solids6
- Ch. 43 - Elementary Particles3
- Ch. 44 - Astrophysics and Cosmology9
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
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Giancoli Douglas 5th editionCh. 02 - Describing Motion: Kinematics in One DimensionProblem 16d
Giancoli Douglas 5th editionCh. 02 - Describing Motion: Kinematics in One DimensionProblem 16dChapter 2, Problem 16d
The position of an object along a straight tunnel as a function of time is plotted in Fig. 2–40. What is its average velocity between t = 25.0 s and t = 30.0 s?
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Identify the formula for average velocity: \( v_{\text{avg}} = \frac{\Delta x}{\Delta t} \), where \( \Delta x \) is the change in position and \( \Delta t \) is the change in time.
From the problem, the time interval is given as \( t_1 = 25.0 \ \text{s} \) and \( t_2 = 30.0 \ \text{s} \). Determine the corresponding positions \( x_1 \) and \( x_2 \) from the graph provided in the figure.
Calculate the change in position: \( \Delta x = x_2 - x_1 \). Substitute the values of \( x_2 \) and \( x_1 \) obtained from the graph.
Calculate the change in time: \( \Delta t = t_2 - t_1 \). Substitute \( t_2 = 30.0 \ \text{s} \) and \( t_1 = 25.0 \ \text{s} \).
Substitute \( \Delta x \) and \( \Delta t \) into the formula for average velocity: \( v_{\text{avg}} = \frac{\Delta x}{\Delta t} \). Simplify the expression to find the average velocity.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Average Velocity
Average velocity is defined as the total displacement divided by the total time taken. It provides a measure of how fast an object is moving in a specific direction over a given time interval. In this case, to find the average velocity between two time points, one must determine the change in position of the object during that time and divide it by the time elapsed.
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Solving Constant and Average Velocity Problems
Displacement
Displacement is a vector quantity that refers to the change in position of an object. It is calculated as the final position minus the initial position and takes into account the direction of movement. In the context of the question, knowing the positions of the object at t = 25.0 s and t = 30.0 s is essential to calculate the displacement needed for the average velocity.
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Time Interval
The time interval is the duration over which an event occurs, measured as the difference between two time points. In this question, the time interval is from t = 25.0 s to t = 30.0 s, which is 5 seconds. Understanding the time interval is crucial for calculating average velocity, as it provides the denominator in the average velocity formula.
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Related Practice
Textbook Question
An airplane travels 1900 km at a speed of 720 km/h, and then encounters a tailwind that boosts its speed to 990 km/h for the next 2700 km. What was the total time for the trip? What was the average speed of the plane for this trip? [Hint: Does Eq. 2–12d apply?]
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Textbook Question
The position of an object is given by 𝓍 = At + Bt², where 𝓍 is in meters and t is in seconds. What are the units of A and B?
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Textbook Question
Sketch the v vs. t graph for the object whose displacement as a function of time is given by Fig. 2–40.
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Textbook Question
A horse trots away from its trainer in a straight line, moving 38 m away in 7.4 s. It then turns abruptly and gallops halfway back in 1.8 s. Calculate its average speed
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Textbook Question
A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 m long. The bowler hears the sound of the ball hitting the pins 2.75 s after the ball is released from his hands. What is the speed of the ball, assuming the speed of sound is 340 m/s?
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