Physics for Scientists and Engineers with Modern Physics, Technology Update
9th Edition
ISBN: 9781305401969
Author: SERWAY, Raymond A.; Jewett, John W.
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 4, Problem 7P
The vector position of a particle varies in time according to the expression
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A particle’s acceleration is (4.0iˆ+3.0jˆ)m/s2.(4.0i^+3.0j^)m/s2. At t = 0, its position and velocity are zero. (a) What are the particle’s position and velocity as functions of time? (b) Find the equation of the path of the particle. Draw the x- and y-axes and sketch the trajectory of the particle.
The vector position of a particle varies in time according to the expression r = 9.00 î - 8.00t? ĵ where r is in meters and t is in seconds.
(a) Find an expression for the velocity of the particle as a function of time, (Use any variable or symbol stated above as necessary.)
m/s
(b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.)
a =
m/s2
(c) Calculate the particle's position and velocity at t = 3.00 s.
ř =
m/s
Type here to search
近
The position of a particle is given by r(t) = (3.0 t2 ˆi+ 5.0 ˆj − 6.0 t ˆk) m. (a) Determine its velocity and acceleration as functions of time. (b) What are its velocity and acceleration at time t = 0? (c) What is the particle’s velocity at t = 2 s?
Chapter 4 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
Ch. 4.1 - Consider the following controls in an automobile...Ch. 4.3 - (i) As a projectile thrown at an upward angle...Ch. 4.3 - Rank the launch angles for the five paths in...Ch. 4.4 - A particle moves in a circular path of radius r...Ch. 4.5 - A particle moves along a path, and its speed...Ch. 4 - Prob. 1OQCh. 4 - Entering his dorm room, a student tosses his book...Ch. 4 - A student throws a heavy red ball horizontally...Ch. 4 - Prob. 4OQCh. 4 - Does a car moving around a circular track with...
Ch. 4 - An astronaut hits a golf ball on the Moon. Which...Ch. 4 - Prob. 7OQCh. 4 - Prob. 8OQCh. 4 - A sailor drops a wrench from the top of a...Ch. 4 - A baseball is thrown from the outfield toward the...Ch. 4 - A set of keys on the end of a string is swung...Ch. 4 - A rubber stopper on the end of a string is swung...Ch. 4 - Prob. 13OQCh. 4 - A spacecraft drifts through space at a constant...Ch. 4 - Prob. 2CQCh. 4 - Prob. 3CQCh. 4 - Describe how a driver can steer a car traveling at...Ch. 4 - A projectile is launched at some angle to the...Ch. 4 - Construct motion diagrams showing the velocity and...Ch. 4 - Explain whether or not the following particles...Ch. 4 - Prob. 1PCh. 4 - When the Sun is directly overhead, a hawk dives...Ch. 4 - Suppose the position vector for a particle is...Ch. 4 - The coordinates of an object moving in the xy...Ch. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - The vector position of a particle varies in time...Ch. 4 - It is not possible to see very small objects, such...Ch. 4 - Prob. 9PCh. 4 - Review. A snowmobile is originally at the point...Ch. 4 - Mayan kings and many school sports teams are named...Ch. 4 - Prob. 12PCh. 4 - In a local bar, a customer slides an empty beer...Ch. 4 - Prob. 14PCh. 4 - A projectile is fired in such a way that its...Ch. 4 - Prob. 16PCh. 4 - Chinook salmon are able to move through water...Ch. 4 - Prob. 18PCh. 4 - The speed of a projectile when it reaches its...Ch. 4 - Prob. 20PCh. 4 - A firefighter, a distance d from a burning...Ch. 4 - Prob. 22PCh. 4 - A placekicker must kick a football from a point...Ch. 4 - A basketball star covers 2.80 m horizontally in a...Ch. 4 - A playground is on the flat roof of a city school,...Ch. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - A student stands at the edge of a cliff and throws...Ch. 4 - Prob. 30PCh. 4 - A boy stands on a diving board and tosses a stone...Ch. 4 - A home run is hit in such a way that the baseball...Ch. 4 - The athlete shown in Figure P4.21 rotates a...Ch. 4 - In Example 4.6, we found the centripetal...Ch. 4 - Prob. 35PCh. 4 - A tire 0.500 m in radius rotates at a constant...Ch. 4 - Review. The 20-g centrifuge at NASAs Ames Research...Ch. 4 - An athlete swings a ball, connected to the end of...Ch. 4 - The astronaut orbiting the Earth in Figure P4.19...Ch. 4 - Figure P4.40 represents the total acceleration of...Ch. 4 - Prob. 41PCh. 4 - A ball swings counterclockwise in a vertical...Ch. 4 - (a) Can a particle moving with instantaneous speed...Ch. 4 - The pilot of an airplane notes that the compass...Ch. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - A police car traveling at 95.0 km/h is traveling...Ch. 4 - A car travels due east with a speed of 50.0 km/h....Ch. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - A river flows with a steady speed v. A student...Ch. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - A farm truck moves due east with a constant...Ch. 4 - A ball on the end of a string is whirled around in...Ch. 4 - Prob. 56APCh. 4 - Prob. 57APCh. 4 - A particle starts from the origin with velocity...Ch. 4 - Prob. 59APCh. 4 - Prob. 60APCh. 4 - Lisa in her Lamborghini accelerates at...Ch. 4 - A boy throws a stone horizontally from the top of...Ch. 4 - Prob. 63APCh. 4 - Prob. 64APCh. 4 - Prob. 65APCh. 4 - Prob. 66APCh. 4 - Why is the following situation impossible? Albert...Ch. 4 - As some molten metal splashes, one droplet flies...Ch. 4 - Prob. 69APCh. 4 - A pendulum with a cord of length r = 1.00 m swings...Ch. 4 - Prob. 71APCh. 4 - A projectile is launched from the point (x = 0, y...Ch. 4 - A spring cannon is located at the edge of a table...Ch. 4 - An outfielder throws a baseball to his catcher in...Ch. 4 - A World War II bomber flies horizontally over...Ch. 4 - Prob. 76APCh. 4 - Prob. 77APCh. 4 - Prob. 78APCh. 4 - A fisherman sets out upstream on a river. His...Ch. 4 - Prob. 80APCh. 4 - A skier leaves the ramp of a ski jump with a...Ch. 4 - Two swimmers, Chris and Sarah, start together at...Ch. 4 - Prob. 83CPCh. 4 - Prob. 84CPCh. 4 - Prob. 85CPCh. 4 - A projectile is fired up an incline (incline angle...Ch. 4 - A fireworks rocket explodes at height h, the peak...Ch. 4 - In the What If? section of Example 4.5, it was...Ch. 4 - Prob. 89CP
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
- v → = ( 6 t − 4 t 2 ) i ^ − 8 j ^. Here v → is in meters per second and t in seconds. (a) What are the position, speed, and acceleration of the particle when t = 4.3 s? (b) When (if ever) is the acceleration zero? Prove your answer. (c) When (if ever) is the velocity zero? Prove your answer.arrow_forwardProblem 2: The position of a particle is given by the following expression, where t is time measured in seconds: r(t) = [(3.65 m/s?)f²]į+ (-4.23 m)j + [(4.48 m/s³)r*]k. Part (a) What is the magnitude of the velocity of the particle, in m/s, at t = 0.00 s? Part (b) What is the magnitude of the velocity of the particle, in m/s, at t = 1.65 s? Part (c) What angle, in degrees, does the velocity of the particle make with the +z axis at t = 1.65 s? Part (d) What is the magnitude of the average velocity, in m/s, betweent = 0.00 s and t = 1.65 s? Part (e) What angle, in degrees, does the average velocity between t = 0.00 s and t = 1.65 s make with the z axis?arrow_forwardThe acceleration of a particle is a constant. At t = 0 the velocity of the particle is (10i ^ + 20j ^ )m/s. At t = 4 s the velocity is 10j ^ m/s. (a) What is the particle’s acceleration? (b) How do the position and velocity vary with time? Assume the particle is initially at the origin.arrow_forward
- An object has an acceleration as a function of time given by (in m/s2): a = (7t2 + 2t) i + (5t3 + 8) j Given: at t=0.0 s, the object is at the origin with a velocity of 0.0 m/s. What is the magnitude of its position (in m) when t= 6 s ?arrow_forwardA fish swimming in a horizontal plane has velocity given by v i j i = 4ˆ + ˆ m/s at a point in theocean where the position relative to a certain rock is r i j i = 10ˆ − 4 ˆ m. After the fish swimswith constant acceleration for 20.0 s, its velocity is v i j = 20ˆ − 5 ˆ m/s.a) What are the components of the acceleration of the fish?b) What is the direction of its acceleration with respect to the unit vector along the x axis?c) If the fish maintains constant acceleration, where is it at t = 25.0 s and in what direction isit moving?arrow_forwardThe acceleration of a particle moving along a straight line is a = (11 - 1.0s) m/s², where s is in meters. If v = 0 when s = 0, determine the magnitude of the particle's velocity when s = 7.0 m.arrow_forward
- An object has position given by the vector r = [3.0m + (6.0m/s)t] i + [2.0m - (2.0m/s2)t2] j, where quantities are in SI units. What is the speed of the object at t = 3.0s?arrow_forwardAn ion's position vector is initially 7 = (-3,9 m )i + (-8.6 m )j + (-3.4 m )k, and 9.3 s later it is 7 = (-2.6 m )i + (7.3 m )ĵ + (1.0 m )R. In unit-vector notation, what is its average velocity during the 9.3 s? Number i k Units m/sarrow_forwardThe velocity of a particle (in meters per second) is given by v = 16t²i + 4t³j+ (5t + 2)k, where t is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle's acceleration when t = 2 s. Also, what is the x, y, z coordinate position of the particle at this instant?arrow_forward
- The vector position of a particle varies in time according to the expression r = 3.00i - 6.00t^2 j, where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (b) Determine the acceleration of the particle as a function of time. (c) Calculate the particles position and velocity at t = 1.00s.arrow_forwardThe vector position of a particle varies in time according to the expressionỉ = 3.00i – 6.00fj, where i is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (b) Determine the accelera- tion of the particle as a function of time. (c) Calculate the particle's position and velocity at t= 1.00 s.arrow_forwarda particle initially at position r=(2j+3k)m moves to r=(2i+3j-2k)m in 2s. Find the magnitude of the particles average velocity. If the particles acceleration is a=(2i-k) m/s^2 , find the angle between the particles acceleration and displacementarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Kinematics Part 3: Projectile Motion; Author: Professor Dave explains;https://www.youtube.com/watch?v=aY8z2qO44WA;License: Standard YouTube License, CC-BY