The position of a particle moving along the x-axis varies with time according to x(t) = 5.0t2 − 4.0t3 m. Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t = 2.0 s, (c) the time at which the position is a maximum, (d) the time at which the velocity is zero, and (e) the maximum position.

The position of a particle moving along the x-axis varies with time according to x(t) = 5.0t2 − 4.0t3 m. Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t = 2.0 s, (c) the time at which the position is a maximum, (d) the time at which the velocity is zero, and (e) the maximum position.

Name: The position of a particle moving along the x-axis varies with time ac
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: The position of a particle moving along the x-axis varies with time according to x(t) = 5.0t2 − 4.0t3 m. Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t = 2.0 s, (c) the time at whic

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 11P: A particle moves along the x axis according to the equation x = 2.00 + 3.00t 1.00t2, where x is in...

See similar textbooks

Similar questions

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.
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.
On a spacecraft two engines fire for a time of 567 s. One gives the craft an acceleration in the x direction of ax = 4.80 m/s2, while the other produces an acceleration in the y direction of ay = 7.52 m/s2. At the end of the firing period, the craft has velocity components of vx = 3751 m/s and vy = 4834 m/s. Calculate the magnitude of the initial velocity.
During the time interval 0 < t < 1, the velocity of an object as a function of time is v = 5 + 3t^2 + 2t^3. Knowing that the object follows a rectilinear trajectory, What is the correct expression for the acceleration?
The velocity of a particle at any time t moving along an x-axis is given by the following equation: v = 3t^2 - 8t + 3 where v is in m/s. At t = 0, x = 0. Determine the following:(a) the particle's displacement between t = 0 and t = 4 s (b) the average velocity for the time interval t =0 to t = 4 s (c) the acceleration when t =3 s (d) the instantaneous velovity at t = 4 s (e) what is the initial direction of motion of the particle?
A particle moves along a straight line such that its position is defined by s=(t^2−6t+5)m. (a) Determine the average velocity of the particle when t = 7.9 s . Express your answer to three significant figures and include the appropriate units. The answer is not 9.8 m/s (b) Determine the average speed of the particle when t = 7.9 s. Express your answer to three significant figures and include the appropriate units. The answer is not 1.9 m/s (c) Determine the acceleration of the particle when t = 7.9 s. Express your answer to three significant figures and include the appropriate units.
A particle moves along an x axis from point A to point B with average velocity v1 = 4.00 m/s through displacement Δx1 = 20.0 m. Then it moves at average velocity v2 through displacement Δx2 = 30.0 m from point B to point C. If the total time is 7.00 s, what is the value of v2?
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.
A particle experiences a constant acceleration, α. At t = T, the particle’s position and speed are observed to be x(t = T) = β and v(t = T) = γ (with the appropriate units), respectively. Find the following quantities in terms of the given quantities (i.e., α, β, γ, and T), i) the initial speed,ii) the initial position,iii) the speed as a function of time, and iv) the position as a function of time.
The acceleration of a particle is given by ax(t)=−2.00m/s2+(3.00m/s3)t. Find the initial velocity v0x such that the particle will have the same x-coordinate at time t = 4.93 s as it had at t=0.
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 of a particle moving along the x axis is given by x = (10 +5t -4.0t2)m, where t is in s. What is the average velocity (in m/s) during the time interval t= 1.0s to t =2.0s