The velocity of a particle is given by v = {16t²i + 4t³j + (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=2s. Also, what is the x, y, z coordinate position of the particle at this instant?

The velocity of a particle is given by v = {16t²i + 4t³j + (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=2s. Also, what is the x, y, z coordinate position of the particle at this instant?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A golf ball is hit off a tee at the edge of a cliff. Its x and y Coordinates as functions of time are given by the following expressions: x = (18.0 m/s)t y = (4.00 m/s)t – (4.90 m/s²)t² a) Express the position of the ball as a function of time in terms of unit vectors. b) Express the velocity of the ball as a function of time in terms of unit vectors. c) Express the acceleration of the ball as a function of time in terms of unit vectors. Note: To express a function in terms of unit vectors, you treat the equivalent of "x" as a coefficient of î, while “y" as a coefficient of j.
1d. A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 18.5 m/s. The cliff is h = 20.0 m above a flat, horizontal beach as shown in the figure. Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.) x= y=
A student standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a stone with velocity v0 = 17 m/s at an angle θ = 27 ° below horizontal. The stone moves without air resistance; use a Cartesian coordinate system with the origin at the stone's initial position. With what speed, vf in meters per second, does the stone strike the ground?
A space shuttle is fired and the position of the shuttle is given by r(t)=(2*t*t-5*t)i+ (3*t+1)j+(12*t*t*t)k where t is in seconds, r is in meters and ij,k are the unit vectors of x,y,z directions respectively. Find the average acceleration of the space shuttle between the time interval t=10 s and t=1 minutes. *
Myla participated in a running competition. She ran around a circular track with a radius of 1.0 x 102 m. Myla completed the track after 2 minutes. If she had a constant speed, what was Myla’s average speed in the entire run? answer in "m·s", please.
A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 17.2t and y = 4.16t − 4.90t2, where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) = m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector as a function of time = m/s(c) obtain the expression for the acceleration vector as a function of time = m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.18 s. = m = m/s = m/s2
A particle starts from the origin at r=0 with a velocity of 8.0 m/s and moves in the xy plane with constant acceleration (3.5i +1.7)) m/s1. (a) When the particle's x coordinate is 27 m, what is its y coordinate? (b) When the particle's x coordinate is 27 r. what is its speed? m/s
The NEXT morning, you wake up in a strange room yet again, and this time you drop a ball from a height of 1.54 m above the floor. The ball hits the floor 0.392 s after your drop it. You guess that you must have been taken to an alien planet with gravity different from Earth s. What is this planet s g (that is, the magnitude of the acceleration due to gravity on this planet)? 10.0 m/s^2 15.0 m/s^2 30.0 m/s^2 20.0 m/s^2
I don't understand how to do this problem. I tried taking the derivative, but that didn't give me the correct answer. I would really appreciate the help. When a 1984 Alpha Romeo Spider sports car accelerates in the x-direction at the maximum possible rate,its motion during the first 20. seconds is extremely well modeled by the simple equation vx2=(60 m2/s3)t, where t is time in seconds and vx is in m/s. In other words, the squareof teh car's velocity increases linearly with time. What is its acceleration after 3s, assuming that the car starts from rest at t=0 s?
At time t = 0, the position vector of a particle moving in the x-y plane is r = 4.62i m. By time t = 0.011 s, its position vector has become (4.84i +0.54j) m. Determine the magnitude Vay of its average velocity during this interval and the angle 0 made by the average velocity with the positive x-axis. Answers: Vav 0= i i m/s
A remote-controlled car is moving around in a level (horizontal) parking lot. The velocity of the car as a function of time is given by: 3 = [5.0m/s – (0.018m/s³)t²]î + [2.0m/s + (0.55m/s²)t]j where î and ĵ are unit vectors representing two perpendicular directions on the horizontal ground (think of them as the East and North directions, if that helps you). b). What are the magnitude and direction of the car's velocity at t = 8.0 s? c). What are the magnitude and direction of the car's acceleration at t = 8.0 s? (Don't be intimated by the velocity function! Look at the î and ĵ components, and work each component separately to begin with, before combining components together to get any resultant vectors, if needed.)
The equation r(t) = (/2t) i+ (/2t- 16t2) j is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t= 0. The angle between the velocity and acceleration vectors at time t = 0 is radians. (Type an exact answer, using n as needed.)