The velocity of a particle is given by v ={16t^2i +4t^3j + (5t +2)k} m/s, where t is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle’s acceleration when t = 2 s. Also, what is the x, y, z coordinate position of the particle at this instant?

The velocity of a particle is given by v ={16t^2i +4t^3j + (5t +2)k} m/s, where t is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle’s acceleration when t = 2 s. Also, what is the x, y, z coordinate position of the particle at this instant?

Name: The velocity of a particle is given by v ={16t^2i +4t^3j + (5t +2)k} m
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: The velocity of a particle is given by v ={16t^2i +4t^3j + (5t +2)k} m/s, where t is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle’s acceleration when t = 2 s. Also, what is the x, y, z coordinate po

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

Figure OQ3.3 shows a birds-eye view of a car going around a highway curve. As the car moves from point 1 to point 2, its speed doubles. Which of the vectors (a) through (e) shows the direction of the cars average acceleration between these two points?
A rock is At t = 0, a particle leaves the origin with a velocity of 12 m/s in the positive x direction and moves in the xy plane with a constant acceleration of (–2i + 4j) m/s2. At the instant the y coordinate of the particle is 18 m, what is the x coordinate of the particle?
If the vector components of the position of a particle moving in the xy plane as a function of time are x = (2.8 m/s2)t2 and y = (6.4 m/s3)t3, at what time t is the angle between the particle's velocity and the x axis equal to 45°?
On a spacecraft two engines fire for a time of 389 s. One gives the craft an acceleration in the x direction of ax = 3.41 m/s^2, while the other produces an acceleration in the y direction of ay = 7.34 m/s^2. At the end of the firing period, the craft has velocity components of vx = 1860 m/s and vy = 4290 m/s. Find the (a) magnitude and (b) direction of the initial velocity. Express the direction as an angle with respect to the +x axis.
A skater is gliding along the ice at 2.2 m/s, when she undergoes an acceleration of magnitude 1.2 m/s2 for 3.0 s. At the end of that time she is moving at 5.8 m/s. (a) What must be the angle between the acceleration vector and the initial velocity vector?
A particle initially is moving at a velocity with Cartesian components (5.0 m/s, 4.0 m/s) and 5.6 s later it is moving at a velocity with components (8.0 m/s, 0.0 m/s). What is the magnitude of its average acceleration, in m/s2?
A dog running in an open field has components of velocity vx = 2.6 m/s and vy = -1.2 m/s at time t1 = 11.7 s . For the time interval from t1 = 11.7 s to t2 = 22.8 s, the average acceleration of the dog has magnitude 0.49 m/s^2 and direction 25.0 measured from the +x−axis toward the +y−axis. At t2, what is the x component, y component, and magnitude of the dog's velocity? What is the direction of the dogs velocity?
The velocity v→ of a particle moving in the xy plane is given by v→=(5.50t-5.00t2)î+9.00ĵ, with v→ in meters per second and t (> 0) in seconds. At t = 1.40 s and in unit-vector notation, At what positive time does the speed equal 10.0 m/s?
The position of a particle is: r(t) = [(4.62 m/s^2) t^2] i + (-3.38m) j + [(4.04 m/s^3) t^3] k What is the magnitude in m/s of the average velocity between t = 0 and t = 1.79s and what angle in degrees does the average velocity make between t = 0s and t = 1.79s
A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.30 s, it is at point (4.40 m, 5.90 m) with velocity (2.70 m/s)ĵ and acceleration in the positive x direction. At time t2 = 12.0 s, it has velocity (–2.70 m/s)î and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit.
A particle leaves the origin with initial velocity v0= 12i + 14j m/s, undergoing constant acceleration a = -0.80i + 0.25j m/s2. If the particle crosses the y-axis at t = 30s and its y-coordinate at the time is 532.5m. How fast is it moving and in what direction is it moving?
At t = 0, a particle leaves the origin with a velocity of 9.0 m/s in the positive ydirection and moves in the xy plane with a constant acceleration of (2.0i - 4.0j)m/s2. At the instant the x coordinate of the particle is 15 m, what is the speedof the particle?