Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 2, Problem 78P
A particle’s position as a function of time is given by x = x0 sinωt, where x0 and ω are constants, (a) Find expressions for the velocity and acceleration, (b) What are the maximum values of velocity and acceleration? (Hint: Consult the table of derivatives in Appendix A.)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
(a) What are the coordinates of the initial position of the stone?
x0
=
m
y0
=
m
(b) What are the components of the initial velocity?
v0x
=
m/s
v0y
=
m/s
(c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not include units in your answer.)
vx
=
vy
=
Q.1
motion of a particle is
The
x = 21 - 18t? + 48t – 16, where x and t are expressed in millimeters
and seconds, respectively. Determine (a) when the velocity is zero,
(b) the position and the total distance traveled when the acceleration is
defined
by
the
relation
zero.
The velocity of a particle is given by v = 23t2 - 110t + 52, where v is in meters per second and t is in seconds. Plot the velocity v and
acceleration a versus time for the first 6.4 seconds of motion and evaluate the velocity when a is zero. Make the plots and then
answer the questions.
Questions:
When t = 0.8 s,
V =
i
m/s,
a =
i
m/s2
When t = 3.7 s,
V =
i
m/s,
a =
i
m/s?
When t = 4.7 s,
V =
i
m/s,
a =
i
m/s?
When a = 0,
V =
m/s
Chapter 2 Solutions
Essential University Physics (3rd Edition)
Ch. 2.1 - We just described three trips from Houston to Des...Ch. 2.2 - The figures show position-versus-time graphs for...Ch. 2.3 - An elevator is going up at constant speed, slows...Ch. 2.5 - Standing on a roof, you simultaneously throw one...Ch. 2.6 - The graph shows acceleration versus time for three...Ch. 2 - Under what conditions are average and...Ch. 2 - Does a speedometer measure speed or velocity?Ch. 2 - You check your odometer at the beginning of a days...Ch. 2 - Consider two possible definitions of average...Ch. 2 - Is it possible to be at position x = 0 and still...
Ch. 2 - Is it possible to have zero velocity and still be...Ch. 2 - If you know the initial velocity v0 and the...Ch. 2 - Starting from rest, an object undergoes...Ch. 2 - In which of the velocity-versus-time graphs shown...Ch. 2 - If you travel in a straight line at 50 km/h for 1...Ch. 2 - If you travel in a straight line at 50 km/h for 50...Ch. 2 - In 2009, Usain Bolt of Jamaica set a world record...Ch. 2 - The standard 26-mile, 385-yard marathon dates to...Ch. 2 - Starting front home, you bicycle 24 km north in...Ch. 2 - The Voyager 1 spacecraft is expected to continue...Ch. 2 - In 2008, Australian Emma Snowsill set an...Ch. 2 - Taking Earths orbit to be a circle of radius 1.5 ...Ch. 2 - Whats the conversion factor from meters per second...Ch. 2 - On a single graph, plot distance versus time for...Ch. 2 - For the motion plotted in Fig. 2.15, estimate (a)...Ch. 2 - A model rocket is launched straight upward. Its...Ch. 2 - A giant eruption on the Sun propels solar material...Ch. 2 - Starting from rest, a subway train first...Ch. 2 - A space shuttles main engines cut off 8.5 min...Ch. 2 - An egg drops from a second-story window, taking...Ch. 2 - An airplanes takeoff speed is 320 km/h. If its...Ch. 2 - ThrustSSC, the worlds first supersonic car,...Ch. 2 - Youre driving at 70 km/h when you apply constant...Ch. 2 - Prob. 29ECh. 2 - An X-ray tube gives electrons constant...Ch. 2 - A rocket rises with constant acceleration to an...Ch. 2 - Starting from rest, a car accelerates at a...Ch. 2 - A car moving initially at 50 mi/h begins slowing...Ch. 2 - In a medical X-ray tube, electrons are accelerated...Ch. 2 - Californias Bay Area Rapid Transit System (BART)...Ch. 2 - Youre driving at speed v0 when you spot a...Ch. 2 - You drop a rock into a deep well and 4.4 s later...Ch. 2 - Your friend is sitting 6.5 m above you on a tree...Ch. 2 - A model rocket leaves the ground, heading straight...Ch. 2 - A foul ball leaves the bat going straight up at 23...Ch. 2 - A Frisbee is lodged in a tree 6.5 m above the...Ch. 2 - Space pirates kidnap an earthling and hold him on...Ch. 2 - You allow 40 min to drive 25 mi to the airport,...Ch. 2 - A base runner can get from first to second base in...Ch. 2 - You can run 9.0 m/s, 20% faster than your brother....Ch. 2 - A jetliner leaves San Francisco for New York, 4600...Ch. 2 - An objects position is given by x = bt + ct3 where...Ch. 2 - An objects position as a function of time t is...Ch. 2 - In a drag race, the position of a car as a...Ch. 2 - Squaring Equation 2.7 gives an expression for v2....Ch. 2 - During the complicated sequence that landed the...Ch. 2 - The position of a car in a drag race is measured...Ch. 2 - A fireworks rocket explodes at a height of 82.0 m,...Ch. 2 - The muscles in a grasshoppers legs can propel the...Ch. 2 - On packed snow, computerized antilock brakes can...Ch. 2 - A particle leaves its initial position x0 at time...Ch. 2 - A hockey puck moving at 32 m/s slams through a...Ch. 2 - Amtraks 20th-Century Limited is en route from...Ch. 2 - A jetliner touches down at 220 km/h and comes to a...Ch. 2 - A motorist suddenly notices a stalled car and...Ch. 2 - A racing car undergoing constant acceleration...Ch. 2 - The maximum braking acceleration of a car on a dry...Ch. 2 - After 35 min of running, at the 9-km point in a...Ch. 2 - Youre speeding at 85 km/h when you notice that...Ch. 2 - Airbags cushioned the Mars rover Spirits landing,...Ch. 2 - Calculate the speed with which cesium atoms must...Ch. 2 - A falling object travels one-fourth of its total...Ch. 2 - Youre on a NASA team engineering a probe to land...Ch. 2 - Youre atop a building of height h, and a friend is...Ch. 2 - A castles defenders throw rocks down on their...Ch. 2 - Two divers jump from a 3.00-m platform. One jumps...Ch. 2 - A balloon is rising at 10 m/s when its passenger...Ch. 2 - Landing on the Moon, a spacecraft fires its...Ch. 2 - Youre at mission control for a rocket launch,...Ch. 2 - Youre an investigator for the National...Ch. 2 - You toss a book into your dorm room, just clearing...Ch. 2 - Consider an object traversing a distance L, part...Ch. 2 - A particles position as a function of time is...Ch. 2 - Ice skaters, ballet dancers, and basketball...Ch. 2 - Youre staring idly out your dorm window when you...Ch. 2 - A police radars effective range is 1.0 km, and...Ch. 2 - An object starts moving in a straight line from...Ch. 2 - Youre a consultant on a movie set, and the...Ch. 2 - (a) For the ball in Example 2.6, find its velocity...Ch. 2 - Your roommate is an aspiring novelist and asks...Ch. 2 - You and your roommate plot to drop water balloons...Ch. 2 - Derive Equation 2.10 by integrating Equation 2.7...Ch. 2 - An objects acceleration increases quadratically...Ch. 2 - An objects acceleration is given by the expression...Ch. 2 - An objects acceleration decreases exponentially...Ch. 2 - A ball is dropped from rest at a height li0 above...Ch. 2 - A wildlife biologist is studying the hunting...Ch. 2 - A wildlife biologist is studying the hunting...Ch. 2 - A wildlife biologist is studying the hunting...Ch. 2 - A wildlife biologist is studying the hunting...Ch. 2 - A wildlife biologist is studying the hunting...
Additional Science Textbook Solutions
Find more solutions based on key concepts
What is the reducing agent in the following reaction?
2 Br –– (aq) + H2 O2 (aq) + 2 H+ (aq) → Br2 (aq) + 2 H2 ...
Chemistry: The Central Science (14th Edition)
Flask A contains yeast cells in glucose-minimal salts broth incubated at 30C with aeration. Flask B contains ye...
Microbiology: An Introduction
What are four functions of connective tissue?
Anatomy & Physiology (6th Edition)
22. For each reaction, calculate how many moles of the product form when 0. 112 mol of the reactant in color co...
Introductory Chemistry (6th Edition)
89. A Lightning Strike
Storm clouds build up large negative charges, as described in the chapter. The charges d...
College Physics: A Strategic Approach (3rd Edition)
10.71 Identify each of the following as an acid or a base: (10.1)
H2SO4
RbOH
Ca(OH)2
HI
...
Chemistry: An Introduction to General, Organic, and Biological Chemistry (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- The magnitude of a particle's velocity is observed to vary with time according to the equation: |v = Bt where Bis a positive constant. What are the units of B? т S m Om: s? O m· .3 marrow_forwardThe acceleration of a particle is a constant. At t = 0 the velocity of the particle is (15.8î + 18.4ĵ) m/s.At = 3.6 s the velocity is 10.5ĵ m/s. (Use the following as necessary: t. Do not include units in your answers.) (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin.arrow_forwardAsap plzzzzzarrow_forward
- A particle with instantaneous velocity V = (2i + 33 + æk) m/s and instantaneous acceleration a = 3ì + 4.53 – 6k m/s² . If path of the particle is a straight line then magnitude of x is: (If numeric value has more than two decimal places, truncate/round off the value to TWo decimal places.)arrow_forwardA common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity on the vertical axis Note that by definition Figure Ux(m/s) 2.0 1.5 1.0 0.5 0 10 20 30 40 50 1 of 1 t(s) What is the displacement Ax of the particle? Express your answer in meters. ► View Available Hint(s) Ax = Submit VE ΑΣΦΑ Part C Previous Answers ? X Incorrect; Try Again; One attempt remaining marrow_forwardA particle moves along the x-axis with position function x(t) = At² + B²²³, where 4 = 3 m s-² and B=ms-3 are constants. Find the instantaneous velocity vx and the instantaneous acceleration ax of the particle at time t = 2 s. Give your answers by entering the appropriate integer numbers in the two empty boxes below (you don't need to concern yourself with significant figures in this question). At time t=2s : Vx = At time t=2s : ax = ms-1. ms-2. You may use the following standard derivative: dc4" dt nCtn - 1 where C and are any constants. narrow_forward
- Please provide the correct answerarrow_forwardThe data set given in Table 2 is expected to obey a non - linear relation x = 1/2 at? You are asked to plot (x) versus (t) such as to obtain a straight line graph. Choose a good set of scales for the data, make a careful and accurate graph, and analyze the graph to obtain the value of the acceleration, a, from the slope. TABLE 2 t (s) | 0.2 0.4 | 0.6 0.8 1.0 1.2 x (m) 0.03 0.12 0.27 0.51 0.77 1.14arrow_forwardThe acceleration of a particle is defined as the relation a = αt-4. Knowing that v = 4m/s when t = 2s and v = -1 m/s when t = 1s, Determine the constant ‘α’. Write the equation of motion when x = 0 at t = 3s.arrow_forward
- A n C D B 02 4 6 8 10 12 position x(m) Part (a) What is the distance traveled, in meters, for path D? X Attempts Remain Part (b) What is the magnitude of the displacement from start to finish, in meters, for path D? Part (c) What is the displacement from start to finish, in meters, for path D?arrow_forwardA point particle of mass m = 1.8 kg moves according to the position function: r(t) = xtai + ytbj + ztck, where t denotes time and x, y, z, a, b, and c are constants such that the exponents are positive integers and the position function has the dimension of length. Part (a) We can write the particle’s velocity function in the form v(t) = ntdi + otej + ptgk. Enter an expression for n in terms of x, y, z, a, b, and c. Part (b) The particle’s velocity function will have the form v(t) = ntdi + otej + ptgk. Enter an expression for d in terms of x, y, z, a, b, and c. Part (c) Here is a set of parameter values for the motion of the particle: m = 1.8 kg, x = 1.8 m/s0, y = 2.4 m/s1, z = 0.15 m/s2, a = 0, b = 1, c = 2. Calculate the x-component of the particle’s angular momentum, in units of kg˙m2/s, about the origin at time t = 1 s. Part (d) Use the same set of parameter values (m = 1.8 kg, x = 1.8 m/s0, y = 2.4 m/s1, z = 0.15 m/s2, a = 0, b = 1, c = 2) to calculate the y-component of…arrow_forwardA particle moves along the h-axis (dimension of length) so that: h = t3 - 3t2 - 45t (in feet, where "t" is in seconds) (a) Plot the h-t, v-t, and a-t graphs in 0 < t < 10 seconds. (b) What is the maximum velocity within this interval?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
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
Kinematics Part 3: Projectile Motion; Author: Professor Dave explains;https://www.youtube.com/watch?v=aY8z2qO44WA;License: Standard YouTube License, CC-BY