Suppose the position of a particle is given by x(t) = (40 m/s)t+ (β/3)t3 – (α/4)t4 where t is time and β and α are constants. Time is measured in seconds. b) The acceleration at t=0, is____ c) The magnitude of the velocity at t=0 is____

Suppose the position of a particle is given by x(t) = (40 m/s)t+ (β/3)t3 – (α/4)t4 where t is time and β and α are constants. Time is measured in seconds. b) The acceleration at t=0, is c) The magnitude of the velocity at t=0 is

Name: Suppose the position of a particle is given by x(t) = (40 m/s)t+ (β/3)
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: Suppose the position of a particle is given by x(t) = (40 m/s)t+ (β/3)t3 – (α/4)t4 where t is time and β and α are constants. Time is measured in seconds.b) The acceleration at t=0, is____c) The magnitude of the velocity at t=0 is____

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 6P: The position of a particle moving along the x axis varies in time according to the expression x =...

See similar textbooks

Similar questions

In a particular Cartesian coordinate system, the y and z-components of the acceleration are zero and the x-component varies as given by the following function: ax(t) = 5t - 2t2 + 45e-t/F, where t is in seconds, ax is in meters per square second, and the constant F is in seconds. At t = 0, the particle was at position x = 3 m with a velocity pointing towards the positive x-axis and having magnitude 35 m/s. In the following problem you can take the constant F = 1.0 s. Find the instantaneous velocity, in meters per second, at t = 2 s. Find the position, in meters, of the particle at t = 1 s. Find the position, in meters, of the particle at t = 3 s.
In a particular Cartesian coordinate system, the y and z-components of the acceleration are zero and the x-component varies as given by the following function: ax(t) = 8t - 2t2 + 15e-t/F, where t is in seconds, ax is in meters per square second, and the constant F is in seconds. At t = 0, the particle was at position x = 3 m with a velocity pointing towards the positive x-axis and having magnitude 25 m/s. In the following problem you can take the constant F = 1.0 s.
Let s(t) = t3 - 30t2 + 18t + 47 be the position function of a car moving along a horizontal line, where t is in seconds and s is in meters. a) Determine the interval when the car is moving to the left. b) Determine the car’s position relative to the origin at the instant if the acceleration is 4 m/s^2 . c) When is the car’s acceleration positive? d) Determine if the speed of the car is increasing or decreasing at t = 4.5 seconds? e) When is the car’s acceleration negative? f) Calculate for the total distance traveled by the car during the first 5 seconds.
In a certain coordinate system, the position of a particle is r= [(3m/s2) i]t2 - [(2m/s4) j] t4 where r is in meters and t is in seconds. a. Find its velocity and acceleration as a function of time. b. Find the magnitude of its velocity and acceleration at t= 2.5s.
A particle moves along the x-axis so that at time t its position is given by x(t) = sin (pi*t^2) for -1<=t <= 1. (A) find the velocity at time t (B) find the acceleration at time t (C) for what values of t does the particle change direction? (D) find all values of t for which the particle is moving left.
The position of a particle moving along the x axis is given by x=3t2-15t-10m, where t is in s, Determine the following a. average velocity during the time interval t=2.5 s to t=4.5s b. instantaneous velocity at 3s c. average acceleration during the time interval t=2.5 s to t=4.5s d. instantaneous acceleration at 3s e. is the particle speeding up or slowing down at 4s? justify your answer
Let s(t) = t3 - 30t2 + 18t + 47 be the position function of a car moving along a horizontal line, where t is in seconds and s is in meters. a) Determine the interval when the car is moving to the left. b) Determine the car’s position relative to the origin at the instant if the acceleration is 4 m/s^2 . c) Determine if the speed of the car is increasing or decreasing at t = 4.5 seconds? d) Calculate for the total distance traveled by the car during the first 5 seconds.
Suppose a particle moving in three-dimensional space has position given by r(t)=⟨2cos(5t),3sin(5t), t2-3ti⟩, 0≤t≤ π . (a) Where is the object located at time t = 0? (b) Find the velocity at time t = 1. (c) Find the acceleration at time t = π/10.
The position of a particle that moves along the x-axis is defined by the equation x=-3t2 +12t-6, where x is in feet and t is in seconds, for the time interval t=0 to t-3 seconds. a. determine the distance traveled by the particle b. maximum value of X c. acceleration of the particle.
At t=0 an object starts from the origin and moves with a constant acceleration of a→=(−3.2i−2.7j)m/s2 on a horizontal surface. If the initial velocity of the object is vo→=(14.1i−18.3j)m/s, determine the magnitude of velocity at t=2.1s. Express your answer in units of m/sm/s using zero decimal places.
Using SI base units, a particle’s position as a function of time is given by x(t)=(7t3+4t2+6) m. (a) At what time will the particle’s acceleration be zero? (b) Find the speed of the particle at that time.
‘The motion of a particle is defined by the relation velocity, and the acceleration of the particle when t t4 - 413 +3t - 2, where x and t are expressed in feet and seconds, respectively. Determine the position, the s