Textbook Question
Estimate the average speed with which the hair on your head grows. Give your answer in both m/s and μm/hour. Briefly describe how you arrived at this estimate.
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Ch 01: Concepts of Motion
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 1, Problem 34
A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jet's acceleration as it speeds up?
Verified step by step guidance1
Step 1: Identify the known quantities in the problem. The initial velocity of the jet is \( v_0 = 300 \; \text{m/s} \), the final velocity is \( v_f = 400 \; \text{m/s} \), and the distance traveled is \( d = 4.0 \; \text{km} \) (convert this to meters: \( d = 4000 \; \text{m} \)).
Step 2: Recall the kinematic equation that relates acceleration, initial velocity, final velocity, and displacement: \( v_f^2 = v_0^2 + 2ad \), where \( a \) is the acceleration and \( d \) is the displacement.
Step 3: Rearrange the equation to solve for acceleration \( a \): \( a = \frac{v_f^2 - v_0^2}{2d} \).
Step 4: Substitute the known values into the equation. Use \( v_0 = 300 \; \text{m/s} \), \( v_f = 400 \; \text{m/s} \), and \( d = 4000 \; \text{m} \).
Step 5: Perform the calculations to find the acceleration \( a \). Ensure that all units are consistent (meters and seconds) and simplify the expression to determine the value of \( a \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Acceleration
Acceleration is defined as the rate of change of velocity of an object with respect to time. It is a vector quantity, meaning it has both magnitude and direction. In this context, acceleration can be calculated by taking the difference in velocity and dividing it by the time taken to achieve that change. Understanding acceleration is crucial for analyzing how quickly the jet plane increases its speed.
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Intro to Acceleration
Kinematics
Kinematics is the branch of mechanics that deals with the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this scenario, kinematic equations can be used to relate the initial and final velocities of the jet, the distance traveled, and the time taken, which are essential for understanding the jet's motion.
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Velocity
Velocity is a vector quantity that describes the rate of change of an object's position. It includes both speed and direction. In the given problem, the initial and final velocities of the jet plane are provided, which are critical for determining how the jet's speed changes over the distance traveled. Understanding velocity is fundamental to analyzing the jet's performance during its acceleration phase.
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Related Practice
Textbook Question
A car traveling at 30 m/s runs out of gas while traveling up a 10° slope. How far up the hill will the car coast before starting to roll back down?
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Textbook Question
For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics. A car starts from rest at a stop sign. It accelerates at 4.0 m/s² for 6.0 s, coasts for 2.0 s, and then slows at a rate of 2.5 m/s² for the next stop sign. How far apart are the stop signs?
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Textbook Question
Perform the following calculations with the correct number of significant figures.
16.5/3.45
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Textbook Question
David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. How far does Tina drive before passing David?
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Textbook Question
Compute the following numbers, applying the significant figure rules adopted in this textbook.
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