A particle moves along the x-axis so that it’s position at any time t≥0t≥0 is given by x(t)=t3−3t2+t+1x(t)=t3−3t2+t+1. For what values of t, 0≤t≤30≤t≤3 , is the particle’s instantaneous velocity the same as its average velocity on the closed interval [0, 3]? Your solution should clearly show all steps leading to the answer as well as justification for it.

A particle moves along the x-axis so that it’s position at any time t≥0t≥0 is given by x(t)=t3−3t2+t+1x(t)=t3−3t2+t+1. For what values of t, 0≤t≤30≤t≤3 , is the particle’s instantaneous velocity the same as its average velocity on the closed interval [0, 3]? Your solution should clearly show all steps leading to the answer as well as justification for it.

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

Section2.1: Average Velocity

Problem 2.1QQ: Under which of the following conditions is the magnitude of the average velocity of a particle...

See similar textbooks

Similar questions

A particle moves along the x-axis so that its velocity at any time t > 0 is given by v(t)=(2π−5)t−sin(πt). A. Find the acceleration at any time t. B. Find the minimum acceleration of the particle over the interval [0,3]. C. Find the maximum velocity of the particle over the interval [0,2].
At t = 0 the coordinates of a particle are x = 0, y = 1.98 m. At a time 0.95 s later, its coordinates are x = 3.21 m, y = 4.20 m. Find the components of the particle's average velocity during this time interval. vx = vy =
The position of an object moving vertically along a line is given by the function s(t) = -4.9t2 + 35t + 22. Find the average velocity of the object over the following intervals. a. [0,1] b. [0,2] c.[0,3] d. [0,h], where h>0 is a real number We haven't talked about obtaining derivative of the function. Is there another way to solve this without obtaining the derivative of the function?
The velocity function of a particle moving along a horizontal line is given by v(t) = ln 2 * 23t , where t ≥ 0 is in seconds. The particle is initially 2/3 units to the left of the origin. Find the position of the particle when the acceleration is equal to 6(ln 2)2 .
The position coordinate of a particle which is confined to move along a straight line is given by "x = 2t3 −24t + 6", where x is measured in meters from a convenient origin and t is in seconds. Determine (a) the time required for the particle to reach a velocity of 72 m/s from its initial condition at t = 0 s, (b) the acceleration of the particle when v = 30 m/s, and (c) the net displacement of the particle during the interval from t = 1 s to t = 4 s.
At time t = 16 s, the velocity of a particle moving in the x-y plane is v = 0.12i + 2.69j m/s. By time t = 16.15 s, its velocity has become -0.07i + 2.56j m/s. Determine the magnitude aav of its average acceleration during this interval and the angle θ made by the average acceleration with the positive x-axis. The angle θ is measured counterclockwise from the positive x-axis.
A particle moves along the yy axis so that its position at any time t, for 0≤t≤5t, is given by y(t)=t4−18t2. Find the intervals in which the particle is speeding up.
A particle moves along the x-axis with position at time t given by x(t) = e^t cos t for 0<= t <= 2pi. Find each time t, for which the particle is at rest.
Under which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval? (a) A particle moves in the +x direction without reversing. (b) A particle moves in the x direction without reversing. (c) A particle moves in the +x direction and then reverses the direction of its motion. (d) There are no conditions for which it is true.
A blue car of length 4.52 m is moving north on a roadway (hat intersects another perpendicular roadway (Fig. P2.81, page 58). The width of the intersection from near edge to far edge is 28.0 m. The blue car has a constant acceleration of magnitude 2.10 m/s2 directed south. The time interval required for the nose of the blue car to move from the near (south) edge of the intersection to the north edge of the intersection is 3.10 s. (a) How far is the nose of the blue car from the south edge of the intersection when it stops? (b) For what time interval is any part of the blue car within the boundaries of the intersection? (c) A red car is at rest on the perpendicular intersecting roadway. As the nose of the blue car enters the intersection, the red car starts from rest and accelerates east at 5.60 m/s2. What is the minimum distance from the near (west) edge of the intersection at which the nose of the red car can begin its motion if it is to enter the intersection alter the blue car has entirely left the intersection? (d) II the red car begins its motion at the position given by the answer to pan (c), with what speed does it enter the intersection?
On a spacecraft two engines fire for a time of 532 s. One gives the craft an acceleration in the x direction of ax = 4.92 m/s2, while the other produces an acceleration in the y direction of ay = 7.16 m/s2. At the end of the firing period, the craft has velocity components of vx = 3743 m/s and vy = 4808 m/s. Calculate the magnitude of the initial velocity.
The position of a particle is given by the function s(t)=2t2+3t−4. Find the time t=c in the interval 0≤t≤4 when the instantaneous velocity of the particle equals to its average velocity in this interval.