Textbook Question
A particle starts from x0 = 10 m at t0 = 0 s and moves with the velocity graph shown in FIGURE EX2.6. What is the object’s position at t = 2 s and 4 s?
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Ch 02: Kinematics in One Dimension
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 2, Problem 11
FIGURE EX2.8 showed the velocity graph of blood in the aorta. What is the blood's acceleration during each phase of the motion, speeding up and slowing down?
Verified step by step guidance1
Step 1: Understand the graph. The graph shows velocity (Vx) on the y-axis and time (t) on the x-axis. The motion is divided into three stages: Stage 1 (speeding up), Stage 2 (slowing down), and Stage 3 (constant velocity). Acceleration is the rate of change of velocity with respect to time, calculated as a = Δv / Δt.
Step 2: Analyze Stage 1 (speeding up). In this stage, velocity increases from 0 m/s to 6 m/s over a time interval of 2 seconds. Use the formula for acceleration: a = (v_final - v_initial) / (t_final - t_initial). Substitute v_initial = 0 m/s, v_final = 6 m/s, t_initial = 0 s, and t_final = 2 s.
Step 3: Analyze Stage 2 (slowing down). In this stage, velocity decreases from 6 m/s to 4 m/s over a time interval of 4 seconds (from t = 2 s to t = 6 s). Use the same formula for acceleration: a = (v_final - v_initial) / (t_final - t_initial). Substitute v_initial = 6 m/s, v_final = 4 m/s, t_initial = 2 s, and t_final = 6 s.
Step 4: Analyze Stage 3 (constant velocity). In this stage, velocity remains constant at 4 m/s from t = 6 s to t = 10 s. Since there is no change in velocity, the acceleration is zero. This can be confirmed using the formula: a = (v_final - v_initial) / (t_final - t_initial), where v_initial = v_final = 4 m/s.
Step 5: Summarize the results. Calculate the acceleration for each stage using the formulas provided. Stage 1 has positive acceleration (speeding up), Stage 2 has negative acceleration (slowing down), and Stage 3 has zero acceleration (constant velocity).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Velocity
Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It has both magnitude and direction, which means it indicates how fast an object is moving and in which direction. In the context of the blood flow in the aorta, the velocity graph shows how the speed of blood changes over time during different phases of its motion.
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Acceleration
Acceleration is the rate of change of velocity over time. It can be positive (speeding up) or negative (slowing down). In the velocity-time graph provided, the slope of the line segments indicates the acceleration during each phase: a steep positive slope indicates increasing speed, while a negative slope indicates decreasing speed. Flat segments indicate constant velocity, meaning zero acceleration.
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Slope of a Graph
The slope of a graph represents the relationship between two variables. In a velocity-time graph, the slope corresponds to acceleration. A positive slope indicates acceleration (speeding up), a negative slope indicates deceleration (slowing down), and a zero slope indicates constant velocity. Analyzing the slopes in the given graph allows us to determine the acceleration of blood during each phase of its motion.
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Related Practice
Textbook Question
FIGURE EX2.8 is a somewhat idealized graph of the velocity of blood in the ascending aorta during one beat of the heart. Approximately how far, in cm, does the blood move during one beat?
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Textbook Question
What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s?
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Textbook Question
FIGURE EX2.12 shows the velocity-versus-time graph for a particle moving along the x-axis. Its initial position is at x0 = 2 m at t0 = 0 s. What are the particle's position, velocity, and acceleration at t = 1.0 s?
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Textbook Question
FIGURE EX2.9 shows the velocity graph of a particle. Draw the particle's acceleration graph for the interval 0 s ≤ t ≤ 4 s.
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Textbook Question
FIGURE EX2.12 shows the velocity-versus-time graph for a particle moving along the x-axis. Its initial position is at x0 = 2 m at t0 = 0 s. What are the particle's position, velocity, and acceleration at t = 3.0 s?
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