Textbook Question
A particle's velocity is described by the function vₓ = (t² - 7t + 10) m/s, where t is in s. What is the particle's acceleration at each of the turning points?
1889
views
Ch 02: Kinematics in One Dimension
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Not the one you use?Change textbookSelect a different textbook
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 38a
A block is suspended from a spring, pulled down, and released. The block's position-versus-time graph is shown in FIGURE P2.38. At what times is the velocity zero? At what times is the velocity most positive? Most negative?
Verified step by step guidance1
Analyze the graph: The position-versus-time graph shows the block's displacement (x) as a function of time (t). Velocity is the slope of the position-time graph at any given point.
Identify times when the velocity is zero: Velocity is zero when the slope of the graph is flat (horizontal). From the graph, this occurs at t = 4 seconds and t = 8 seconds.
Determine times when the velocity is most positive: Velocity is most positive when the slope of the graph is steepest and positive. From the graph, this occurs between t = 0 and t = 2 seconds, with the steepest slope at t = 2 seconds.
Determine times when the velocity is most negative: Velocity is most negative when the slope of the graph is steepest and negative. From the graph, this occurs between t = 8 seconds and t = 10 seconds, with the steepest slope at t = 10 seconds.
Summarize findings: The velocity is zero at t = 4 seconds and t = 8 seconds, most positive at t = 2 seconds, and most negative at t = 10 seconds. These observations are based on the slopes of the graph at these points.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
8mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Position-Time Graph
A position-time graph illustrates the position of an object over time. The slope of the graph at any point indicates the object's velocity. A horizontal line indicates zero velocity, while a positive slope indicates positive velocity and a negative slope indicates negative velocity. Understanding how to interpret these slopes is crucial for analyzing motion.
Recommended video:
Guided course
03:04
Curved Position-Time Graphs & Acceleration
Velocity
Velocity is the rate of change of position with respect to time and is a vector quantity, meaning it has both magnitude and direction. It can be calculated as the slope of the position-time graph. When the graph is flat, the velocity is zero; when the graph slopes upwards, the velocity is positive, and when it slopes downwards, the velocity is negative.
Recommended video:
Guided course
7:27Escape Velocity
Equilibrium and Oscillation
In the context of a spring system, equilibrium refers to the position where the forces acting on the block are balanced. When the block is pulled down and released, it oscillates around this equilibrium position. The analysis of the position-time graph helps identify the points in time when the block is at rest (velocity zero) and when it is moving fastest in either direction.
Recommended video:
Guided course
10:13Torque & Equilibrium
Related Practice
Textbook Question
The vertical position of a particle is given by the function y = (t2 - 4t + 2) m, where t is in s. What is the particle's position at that time?
2348
views
Textbook Question
A particle's velocity is described by the function vₓ =kt² m/s, where k is a constant and t is in s. The particle's position at t₀ = 0 s is x₀ = -9.0 m. At t₁ = 3.0 s, the particle is at x₁ = 9.0 m. Determine the value of the constant k. Be sure to include the proper units.
2827
views
Textbook Question
The position of a particle is given by the function x = (2t3 = 6t2 + 12) m, where t is in s. At what time does the particle reach its minimum velocity? What is (vx)min?
2612
views
1
rank
Textbook Question
A block is suspended from a spring, pulled down, and released. The block's position-versus-time graph is shown in FIGURE P2.38. Draw a reasonable velocity-versus-time graph.
1643
views
Textbook Question
The position of a particle is given by the function x = (2t3 - 6t2 + 12) m, where t is in s. At what time is the acceleration zero?
2275
views