A particle's position is given as [(2.00 + 0.500 sin(0.4001))î + (3.00 + 0.500 sin(0.4004))ĵ] + 2.00/²k) m,where the angles in the equation are given in radians, the time in seconds and the position in meters.(a) Determine the position of the particle at t = 0.(b) Determine the speed of the particle at t = 0.200 s.(c) Determine the average acceleration of the particle betweent = 0.200 s and t = 0.400 s.

Given: x(t) = [2.00+0.500 sin(0.400t)]i^ + 3.00+0.500 sin(0.400t)j^ +2.00t2 k^

Answered: A particle's position is given as…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by the following expressions: x = (18.0 m/s)t y = (4.00 m/s)t – (4.90 m/s²)t² (a) Express the position of the ball as function of time in terms of unit vectors. (b) In terms of unit vectors, calculate for the position, velocity, and acceleration of the golf ball at t = 3.00 s.
The position of an object in circular motion is modeled by the given parametric equations, where t is measured in seconds. x=7sin((pi/8)t), y=-7cos((pi/8)t) How long (in sec) does it take to complete one revolution?
A remote-controlled car is moving around in a level (horizontal) parking lot. The velocity of the car as a function of time is given by: 3 = [5.0m/s – (0.018m/s³)t²]î + [2.0m/s + (0.55m/s²)t]j where î and ĵ are unit vectors representing two perpendicular directions on the horizontal ground (think of them as the East and North directions, if that helps you). b). What are the magnitude and direction of the car's velocity at t = 8.0 s? c). What are the magnitude and direction of the car's acceleration at t = 8.0 s? (Don't be intimated by the velocity function! Look at the î and ĵ components, and work each component separately to begin with, before combining components together to get any resultant vectors, if needed.)
The equation r(t) = (/2t) i+ (/2t- 16t2) j is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t= 0. The angle between the velocity and acceleration vectors at time t = 0 is radians. (Type an exact answer, using n as needed.)
The figure shows the path taken by a drunk skunk over level ground, from initial point i to final point f. The angles are 01-32.0°, e2 = 49.0°, and 03 = 84.0°, and the distances are di 4.80 m, d2 = 7.30 m, and d3 = 10.0 m. What are the (a) magnitude and (b) angle of the skunk's displacement from i to f? Give the angle as a positive (counterclockwise) or negative (clockwise) angle of magnitude less than 180°, measured from the +x direction. dz dg (a) Number 5.586 Units (b) Number 135 Units * (degrees)
A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 17.0t and y = 4.20t − 4.90t2, where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) = m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector as a function of time = m/s(c) obtain the expression for the acceleration vector as a function of time = m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.24 s. = m = m/s = m/s2
An object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.
A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by the following expressions: 2. x = (18.0 m/s)t and y = (4.00 m/s)t – (4.90 m/s²) t² (a) Write a vector expression for the ball's position as a function of time, using the unit vectors i and j. By taking derivatives, obtain expressions for (b) the velocity vector v as a function of time and (c) the acceleration vector a as a function of time. Next use unit-vector notation to write ex- pressions for (d) the position, (e) the velocity, and (f) the acceleration of the golf ball, all at t = 3.00 s.
A particle travels in a circular path of diameter 2250 cm. It has a constant speed and an acceleration of 20 m/s.(a) What is the magnitude of the speed? (b) How long does it take for the particle to complete one trip around the circular path (its period)?
A small metal ball is kicked from the edge of a cliff. Its x- and y-coordinates as functions of time are given by x = 19.9t and y = 3.60t - 4.90t2, where x and y are in meters and t is in seconds. (Do not include units in your answer.) (a) Write a vector expression for the ball's position as a function of time (in m), using the unit vectors î and ĵ. (Give the answer in terms of t.) r = By taking derivatives, do the following. (b) Obtain the expression for the velocity vector v as a function of time (in m/s). (Give the answers in terms of t.) V = a = (c) Obtain the expression for the acceleration vector a as a function of time (in m/s²). m/s² m r = (d) Next, use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the metal ball at t = 2.76 s. (Assume the position is in m, the velocity is in m/s and the acceleration is in m/s².) ✓ = m/s a m m/s m/s²
You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (-140 m, 30 m). The x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (bx and -70), then (-20 and cy), then (-60 and -70). What are (a) component bx and (b) component cy? What are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement?
The position r of a particle moving in an xy plane is given by ř seconds. In unit-vector notation, calculate (a) 7, (b) V , and (c) a for t = 3.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 3.00 s? Give your answer in the range of (-180°; 180°). (4.00r3 – 1.00t)î + (5.00 – 1.00r4)j with 7 in meters and t in (a) Number i i Units (b) Number ît i Units i (c) Number i i Units (d) Number i Units

SEE MORE QUESTIONS

Recommended textbooks for you

College Physics

Physics

ISBN:

9781305952300

Author:

Raymond A. Serway, Chris Vuille

Publisher:

Cengage Learning

University Physics (14th Edition)

Physics

ISBN:

9780133969290

Author:

Hugh D. Young, Roger A. Freedman

Publisher:

PEARSON

Introduction To Quantum Mechanics

Physics

ISBN:

9781107189638

Author:

Griffiths, David J., Schroeter, Darrell F.

Publisher:

Cambridge University Press

College Physics

Physics

ISBN:

9781305952300

Author:

Raymond A. Serway, Chris Vuille

Publisher:

Cengage Learning

University Physics (14th Edition)

Physics

ISBN:

9780133969290

Author:

Hugh D. Young, Roger A. Freedman

Publisher:

PEARSON

Introduction To Quantum Mechanics

Physics

ISBN:

9781107189638

Author:

Griffiths, David J., Schroeter, Darrell F.

Publisher:

Cambridge University Press

Physics for Scientists and Engineers

Physics

ISBN:

9781337553278

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

Lecture- Tutorials for Introductory Astronomy

Physics

ISBN:

9780321820464

Author:

Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden

Publisher:

Addison-Wesley

College Physics: A Strategic Approach (4th Editio…

Physics

ISBN:

9780134609034

Author:

Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher:

PEARSON

SEE MORE TEXTBOOKS