Example 3• A particle moves along the x-axis so that at any t≥ 0 its velocity is given by v(t) = t² - 16t+4. What is the velocityof the particle when its acceleration is zero.

Name: Example 3• A particle moves along the x-axis so that at any t≥ 0 its
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: Example 3• A particle moves along the x-axis so that at any t≥ 0 its velocity is given by v(t) = t² - 16t+4. What is the velocityof the particle when its acceleration is zero.

Given data: Velocity as function of time v(t) = t2 - 16t + 4 Required: The velocity of the particle…

Answered: A particle moves along the x-axis so…

Science

Physics

A particle moves along the x-axis so that at any t 20 its velocity is given by v(t) = t²- 16t+4. What is the velocity of the particle when its acceleration is zero.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 7CQ

See similar textbooks

Related questions

Q: F12-19. A particle is traveling along the parabolic path y = 0.25x. If x = 8 m, v, = 8 m/s, and a̟ =…

A: Write the given relation between x and y and differentiate both sides wrt time. Plug the knowns in…

Q: A particle starts moving from the origin in xy-plane with initial velocity = –2î +6j m/s. If the…

A: Given data The initial velocity is given as v1→=-2i^+6j^ m/s. The final velocity is given as…

Q: particle initially is moving at a velocity with Cartesian components (5.0 m/s, 4.0 m/s) and 5.6 s…

A: Given u̅ =( 5î +4 ĵ ) v̅ = 8 î t = 5.6 s

Q: The position of a particle in space at time tis: r(t) = (sec(t)) * i + (tan t) * j + 4/3 tk. Write…

A: Given: The position of the particle is rt=secti+tantj+43tk…

Q: The velocity of a particle is given by v = {16t²i + 4t³j + (5t +2)k}m/s, where t is in seconds. If…

Q: An ion's position vector is initially r==(5i-6j+2k)m, and 10 s later it is r=(-2i+8j-2k)m.In…

Q: How far from the origin has the particle gone after 0.11 minutes if Vx = 3m/s , Vy = 2 m/s and Vz =…

A: Given: vx=3 m/svy = 2 m/svz = 3.31 m/st = 0.11 m

Q: If a particle moving in a circular path of radius 8.1 m has a velocity function v = 3.5t 2 (units:…

Q: A particle moves in the xy-plane with a constant acceleration given by a = -4 j. At t= 0, the…

Q: has an acceleration of a=4i + (t-2)j The velocity at t=0 is v0=-2i + 0j and is at the origin at t=0…

A: We know that the let the x and y directions are independent and can be treated separately. Now in…

Q: A particle trajectory is described by x= ( 0.7t° -5.7 t ) m, and y=(1t-4.4 t) m. where t is in…

A: Particle's trajectory: x=0.7t3-5.7t2y=1t2-4.4t 1) At t=4.2 s Plugging value of t in given equations…

Q: A particle P starts at time t = 0 s at the position x = -13 m y = -10 m. The velocity of the…

Q: A particle moves in xy plane with a constant acceleration. At t = 0 the particle at = (4.0m)i +…

A: With uniform acceleration, there are three standard equations of motion as given below. v=u+at…

Q: The velocity of a particle is given by v- [16t'i + 4t'j + (5t + 2)k) m/s, where t is in seconds. If…

Q: A particle moves in one dimension according to the equation: x(t)= 2.0m + (5.0m/s)t - (6.2m/s2)t2.…

Q: A body moves in space , the location vector r = 2t i +tj +2 k m, How much the velocity of it at 2…

A: Given that, The position of the body, r=2t2i+tj+2k m We know that, Velocity, v=drdt

Q: A particle starts at the origin (x = 0) and moves in one dimension. The figure shows the velocity of…

A: Given: a velocity time graph

Q: A particle starts from the origin at t=0 with a velocity of 8.0 m/s and moves in the xy plane with…

A: Given Data :Initial speed u→ = (8 j^ ) msacceleration a→ = 3.5 i^+1.7 j^ ms2Let i^ denotes the…

Q: The velocity of a particle is given by v ={16t^2i +4t^3j + (5t +2)k} m/s, where t is in seconds. If…

A: The acceleration along the X direction can be written as ax=dvxdtax=ddt16t2ax=32t…

Q: A particle moving along the x-axis has velocity function v(t) = t³ sin t. How far does the particle…

A: We are given the velocity as function of time. We know that velocity is given as v=dxdt We thus…

Q: At time t = 0 a particle at the origin of an xyz-coordinate system has a velocity vector of vo =…

A: Equation of motion for the given condition is v=v0+at

Q: The velocity of a particle is defined by v,= 100 - t and v, = 100 +10t - 2t where v is in feet per…

A: Given that, vx=100-t32vy=100+10t-2t2 The formula to calculate the radius of curvature is given as…

Q: A particle moves along the x-axis. The function x(t) gives the particle's position at any time t2 0:…

Q: A particle’s velocity along the x-axis is described by v(x) = A x + B x2, where x is in meters, v is…

Q: A particle moves along a circular path having a radius of 1.1 m. At an instant when the speed of the…

Q: The equation r(t) = ( sin t) i + ( cost)j + (t) k is the position of a particle in space at time t.…

A: The velocity of a particle is the rate of change of displacement with respect to time. That is,…

Q: 3. A one dimensional problem. Assume v = v(t) = Determine the position and acceleration at time t =…

Q: The velocity v of a particle moving in the xy plane is given by v=(6t-4t2)i+8j,with v in meters per…

Q: A particle moving in the x-y plane has a velocity v = 7.80i +2.97j m/s at a certain instant. If the…

Q: wing along a circle of radius r= 4 m, is v(t) = 4t²; where v is in m/s and t is in s. The magnitude…

Q: At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive ydirection and…

A: The equation of motion is given by,

Concept explainers

Displacement, Velocity and Acceleration

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

Linear Displacement

The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.

Topic Video

Question

Example 3
• A particle moves along the x-axis so that at any t≥ 0 its velocity is given by v(t) = t² - 16t+4. What is the velocity
of the particle when its acceleration is zero.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

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

can u solve thıs questıon
If the velocity of a particle is nonzero, can the particle’s acceleration be zero? Explain.
• 4. An object's position is described by the following polynomial for O s to 10 s. S (t) = t3 - 15 t2 + 54 t where Sin meters, %3D t is in seconds. Determine : a) The object's Velocity Function3; b) The object's acceleration Function; c) The object's position at, t = 4 s; d) The object's velocity at, t = 4 s; %3D e) The object's acceleration at t = 4s; f) The time and velocity when object returns to its original position; g) The time and velocity when acceleration is zero. h) Is the object's speed is increasing, decreasing, either if time is 4 s ? - NOTES E UELDIMDDOVE OFFICE
7) A particle moves along a plane circular path of radius r equal to 1 ft. The position OA is given as a function of time as 0 = 6 sin(5t) rad, where t is in seconds. What are the rectangular compo- nents of velocity and acceleration for the particle at t = = sec? 8
QUESTION 7 A particle at point (2,3) has a velocity v = (3î + 5ĵ) m/s. It moves with constant acceleration of a = ( – 1.5î – 4.5 ĵ ) m/s². What are its coordinates after 4 seconds? (5,4) Impossible to calculate from given data. O (57 – 4.57) m (2, -13)
• An object travels along a straight path, So = 0 and Vo = 0, it's acceleration in m/s² as a function of time is given. Construct the s-t, v-t and a-t motion graphs. %3D (0.41 0st<10s @ a ={2.4 10 si<20s ® O 20
thanks for help
Differential Equation "Rectilinear motion And Escape Velocity " (TOPIC) Please show solutions Thankyouu!
EXAMPLE 34 The acceleration a of a particle moving with an initial velocity u varies with distance x as a=kVx wherek is a constant. The distance covered by the particle when its velocity becomes 3u is given by 2 \2/3 3u? (a) k (b) (3ku²)^3 4/3 2/3 2 2/3 (c) k (d) 0 amiT 3k
A celebrated Mark Twain story has motivated contestants in the Calaveras County Jumping Frog Jubilee, where frog jumps as long as 2.2 m have been recorded. If a frog jumps 2.2 m and the launch angle is 45, find (a) the frogs launch speed and (b) the time the frog spends in the air. Ignore air resistance.
A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m). (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P3.46. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure P3.46
(a) Repeat the problem two problems prior, but for the second leg you walk 20.0 m in a direction 40.0° north of east (which is equivalent to subtracting B from A that is, to finding R=AB ). (b) Repeat the problem two problems prior, but now you first walk 20.0 m in a direction 40.0° south of west and then 12.0 m in a direction 20.0° east of south (which is equivalent to subtracting A from B that is, to finding R=BA=R ). Show that this is the case.