Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 4, Problem 3P
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 solution
Students 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.
A particle moving with an initial velocity v, = (10m/s)î and initial position 7, = (4m)î + (2m)j,
undergoes an acceleration ở = 2t²î + 4ĵ in SI units.
For t = 10 s;
a) Calculate the velcoity v= vxI+ vy®.
b) Calculate the position r= x+ y.
c) What are the magnitudes of the velocity and the position vector of
the particle?
d) Find also the angle each vector is making with the x-axis at that
time.
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
Chapter 4 Solutions
Physics for Scientists and Engineers with Modern Physics
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 - Suppose the position vector for a particle is...Ch. 4 - The coordinates of an object moving in the xy...Ch. 4 - The vector position of a particle varies in time...Ch. 4 - It is not possible to see very small objects, such...Ch. 4 - Review. A snowmobile is originally at the point...
Ch. 4 - In a local bar, a customer slides an empty beer...Ch. 4 - Mayan kings and many school sports teams are named...Ch. 4 - A projectile is fired in such a way that its...Ch. 4 - The speed of a projectile when it reaches its...Ch. 4 - Prob. 10PCh. 4 - A firefighter, a distance d from a burning...Ch. 4 - A basketball star covers 2.80 m horizontally in a...Ch. 4 - A student stands at the edge of a cliff and throws...Ch. 4 - Prob. 14PCh. 4 - A home run is hit in such a way that the baseball...Ch. 4 - Prob. 16PCh. 4 - A boy stands on a diving board and tosses a stone...Ch. 4 - In Example 4.6, we found the centripetal...Ch. 4 - The astronaut orbiting the Earth in Figure P4.19...Ch. 4 - An athlete swings a ball, connected to the end of...Ch. 4 - The athlete shown in Figure P4.21 rotates a...Ch. 4 - A tire 0.500 m in radius rotates at a constant...Ch. 4 - (a) Can a particle moving with instantaneous speed...Ch. 4 - A ball swings counterclockwise in a vertical...Ch. 4 - Prob. 25PCh. 4 - The pilot of an airplane notes that the compass...Ch. 4 - You are taking flying lessons from an experienced...Ch. 4 - A car travels due east with a speed of 50.0 km/h....Ch. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - A river flows with a steady speed v. A student...Ch. 4 - You are participating in a summer internship with...Ch. 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. 35APCh. 4 - A particle starts from the origin with velocity...Ch. 4 - Lisa in her Lamborghini accelerates at...Ch. 4 - A boy throws a stone horizontally from the top of...Ch. 4 - Why is the following situation impossible? Albert...Ch. 4 - As some molten metal splashes, one droplet flies...Ch. 4 - Prob. 41APCh. 4 - A pendulum with a cord of length r = 1.00 m swings...Ch. 4 - A spring cannon is located at the edge of a table...Ch. 4 - A projectile is launched from the point (x = 0, y...Ch. 4 - A fisherman sets out upstream on a river. His...Ch. 4 - An outfielder throws a baseball to his catcher in...Ch. 4 - Prob. 47APCh. 4 - You are on the Pirates of the Caribbean attraction...Ch. 4 - A skier leaves the ramp of a ski jump with a...Ch. 4 - A projectile is fired up an incline (incline angle...Ch. 4 - Two swimmers, Chris and Sarah, start together at...Ch. 4 - In the What If? section of Example 4.5, it was...Ch. 4 - A fireworks rocket explodes at height h, the peak...
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
- A particle is moving in three dimensions and its position vector is given by; r(t) = (4t² + 1.7t) î + (1.5t − 2.1)ĵ + (2.7t³ + 2t) k where r is in meters and t is in seconds. Determine the magnitude of the instantaneous velocity at t = 3s. Express your answer in units of m/s using one decimal place. 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_forwardAn 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_forward
- A 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_forwardAn 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_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 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 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_forwardThe position vector of a particle is given as r = (t^2-6t+8)i + (t^2-9)j Find the magnitude and direction of the particle’s position, velocity, and acceleration at ? = 2?. Find the magnitude and direction of the particle’s displacement, average velocity and average acceleration for the time period ? = 2? to ? = 3?.arrow_forward
- A particle moving along the x-axis has its position described by the function x =( 5.00 t^3-5.00t+t+ 1.00 )m, where t is in s. At t= 4.00, what are the particle's (a) position, (b) velocity, and (c) acceleration?arrow_forwardThe acceleration of a particle is given by a = 2t - 15, where a is in meters per second squared and t is in seconds. Determine the velocity and displacement as functions of time. The initial displacement at t = 0 is 5o = -6 m, and the initial velocity is vo= 5 m/s. Once you have determined the functions of time, answer the questions. Questions: When t = 4.9 s, S= i V= a= i i m m/s m/s²arrow_forwardThe position of a particle moving along the x axis varies in time according to the expression x = 6t 2, where x is in meters and t is in seconds. Evaluate its position at the following times. (a) t = 2.40 s (b) t = 2.40s + At Xf = (c) Evaluate the limit of Ax/At as At approaches zero to find the velocity at t = 2.40 s. m/sarrow_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