Domanda del libro di testo
A particle moving along the x-axis has its position described by the function x = (2t3 + 2t + 1) m, where t is in s. At t = 2s, what are the particle's position?
2244
views
Ch 02: Kinematics in One Dimension
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 2, Problema 31
FIGURE EX2.31 shows the acceleration-versus-time graph of a particle moving along the x-axis. Its initial velocity is v0x = 8.0 m/s at t0 = 0 s. What is the particle’s velocity at t = 4.0s?
Guida verificata passo dopo passo1
Step 1: Understand the relationship between acceleration, velocity, and time. The velocity of a particle can be determined by integrating the acceleration over time. Mathematically, this is expressed as: , where is the initial velocity, and is the acceleration as a function of time.
Step 2: Analyze the acceleration-versus-time graph provided in the problem. Break the graph into segments where the acceleration is constant or changes linearly. For each segment, determine the mathematical expression for acceleration or its constant value.
Step 3: Compute the change in velocity for each segment by integrating the acceleration over the corresponding time interval. For a constant acceleration, the change in velocity is given by . For a linearly changing acceleration, use the appropriate integration formula.
Step 4: Add the changes in velocity from all segments to the initial velocity to find the final velocity at .
Step 5: Verify the units and ensure the final velocity is consistent with the graph's trends. This involves checking that the direction and magnitude of the velocity align with the acceleration's behavior over time.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
6mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Acceleration
Acceleration is 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 the context of the acceleration-versus-time graph, the area under the curve represents the change in velocity over a specific time interval.
Video consigliato:
Percorso guidato
05:47
Intro to Acceleration
Velocity
Velocity is the speed of an object in a specified direction. It is also a vector quantity and can be calculated by integrating acceleration over time. Given the initial velocity and the change in velocity from the acceleration graph, the final velocity can be determined at any point in time.
Video consigliato:
Percorso guidato
7:27Escape Velocity
Integration of Acceleration
To find the velocity from an acceleration-time graph, one must integrate the acceleration function over the desired time interval. This process involves calculating the area under the acceleration curve, which directly gives the change in velocity, allowing us to update the initial velocity to find the final velocity at a specific time.
Video consigliato:
Percorso guidato
11:43Finding Moment Of Inertia By Integrating
Pratica correlata
Domanda del libro di testo
A bicycle coasting at 8.0 m/s comes to a 5.0-m-long, 1.0-m-high ramp. What is the bicycle's speed as it leaves the top of the ramp?
2623
views
Domanda del libro di testo
A skier is gliding along at 3.0 m/s on horizontal, frictionless snow. He suddenly starts down a 10° incline. His speed at the bottom is 15 m/s. What is the length of the incline?
2264
views
1
rank
Domanda del libro di testo
FIGURE EX2.32 shows the acceleration graph for a particle that starts from rest at t = 0 s. What is the particle's velocity at t = 6 s?
1473
views
Domanda del libro di testo
A particle moving along the x-axis has its veocity described by the function vx = 2t2 m/s, where t is in s. itsinitial position is x0 = 1 m at t0 = 0 s. At t = 1 s, what are the particle's position?
2217
views
Domanda del libro di testo
A snowboarder glides down a 50-m-long, 15° hill. She then glides horizontally for 10 m before reaching a 25° upward slope. Assume the snow is frictionless. How far can she travel up the 25° slope?
2040
views