Skip to main content
Ch 02: Kinematics in One Dimension
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 02: Kinematics in One DimensionProblema 33a
Capitolo 2, Problema 33a

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?

Guida verificata passo dopo passo
1
Step 1: Identify the given position function of the particle, which is x(t) = 2t^3 + 2t + 1 (in meters), where t is in seconds.
Step 2: To find the position of the particle at t = 2s, substitute t = 2 into the position function x(t). This means you will calculate x(2) = 2(2)^3 + 2(2) + 1.
Step 3: Simplify the expression by evaluating the powers and performing the arithmetic operations. Start with the cubic term, then the linear term, and finally add the constant term.
Step 4: After simplifying, the result will give you the position of the particle in meters at t = 2s.
Step 5: Ensure the units are consistent and the final position is expressed in meters, as the problem specifies the position in meters.

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:
2m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Position Function

The position function describes the location of a particle along a specific axis as a function of time. In this case, the position is given by the equation x = (2t^3 + 2t + 1) m, where 't' represents time in seconds. Understanding this function is crucial for determining the particle's position at any given time.
Video consigliato:
Percorso guidato
08:30
Intro to Wave Functions

Evaluating Functions

Evaluating a function involves substituting a specific value for the variable to find the corresponding output. For the position function x(t), substituting t = 2 seconds allows us to calculate the exact position of the particle at that moment. This process is fundamental in physics for analyzing motion.
Video consigliato:
Percorso guidato
08:30
Intro to Wave Functions

Kinematics

Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. It involves concepts such as position, velocity, and acceleration. In this question, understanding kinematics helps in interpreting the position function and its implications for the particle's movement along the x-axis.
Video consigliato:
Percorso guidato
08:25
Kinematics Equations
Pratica correlata
Domanda del libro di testo

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
Domanda del libro di testo

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?

1178
views
1
rank
Domanda del libro di testo

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
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