Textbook Question
Problems 49, 50, 51, and 52 show a partial motion diagram. For each: Draw a pictorial representation for your problem.
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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 43
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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Draw a horizontal axis to represent the motion of both David and Tina. Label the axis as 'distance' (x-axis) and 'time' (y-axis).
Represent David's motion as a straight line starting from the origin, since he is moving at a constant velocity of 30 m/s. The slope of this line corresponds to his velocity.
Represent Tina's motion as a curve starting from the origin, since she begins at rest and accelerates at a constant rate of 2.0 m/s². The curve should show increasing steepness over time, as her velocity increases.
Mark the point where Tina's curve intersects David's straight line. This intersection represents the moment when Tina passes David, as their positions (distances) are equal at that time.
Label key points on the graph, such as Tina's initial position (rest), David's constant velocity, and the intersection point where Tina overtakes David. This pictorial representation will help visualize the problem without solving it mathematically.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Relative Motion
Relative motion refers to the calculation of the motion of an object as observed from another moving object. In this scenario, understanding how David's constant speed of 30 m/s compares to Tina's acceleration is crucial. It helps in visualizing how their positions change over time, which is essential for determining when Tina will catch up to David.
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04:27
Intro to Relative Motion (Relative Velocity)
Acceleration
Acceleration is the rate of change of velocity of an object over time. In this problem, Tina accelerates at a steady rate of 2.0 m/s², meaning her speed increases consistently as time progresses. This concept is vital for understanding how quickly Tina can close the gap between her and David, who is moving at a constant speed.
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05:47Intro to Acceleration
Kinematic Equations
Kinematic equations describe the motion of objects under constant acceleration. Although the question does not require solving the problems mathematically, familiarity with these equations is important for visualizing the relationship between distance, velocity, acceleration, and time. They provide a framework for understanding how far Tina travels as she accelerates compared to David's constant motion.
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08:25Kinematics Equations
Related Practice
Textbook Question
Problems 49, 50, 51, and 52 show a partial motion diagram. For each: Complete the motion diagram by adding acceleration vectors.
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Textbook Question
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?
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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
Problems 44, 45, 46, 47, and 48 show a motion diagram. For each of these problems, write a one or two sentence 'story' about a real object that has this motion diagram. Your stories should talk about people or objects by name and say what they are doing.
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