The eguation r(t)= (3t+ 9) i + (8t - 2) j+(4t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t= 0 as a product of its speed and direction. What is the velocity vector? v(t) = (D i+ (Di+ k
The eguation r(t)= (3t+ 9) i + (8t - 2) j+(4t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t= 0 as a product of its speed and direction. What is the velocity vector? v(t) = (D i+ (Di+ k
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
Chapter3: Motion In Two Dimensions
Section: Chapter Questions
Problem 6P: At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of...
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![The eguation r(t)= (3t+ 9) i + (8t - 2) j+(4t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then
write the particle's velocity at t= 0 as a product of its speed and direction.
What is the velocity vector?
v(t) = (D i+ (Di+ k](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a650aad-3e5f-439d-b570-88193f61b271%2F0fad54be-9a7c-4336-84d8-33b60672c762%2Fdmy8w6z5.jpeg&w=3840&q=75)
Transcribed Image Text:The eguation r(t)= (3t+ 9) i + (8t - 2) j+(4t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then
write the particle's velocity at t= 0 as a product of its speed and direction.
What is the velocity vector?
v(t) = (D i+ (Di+ k
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Introduction:
Kinematics helps to find out the velocity, acceleration of the particle at any time t when position of the particle is given. The relation between displacement, velocity and acceleration helps to find the unknown quantity.
Given data:
The position of the particle in the space at time t is,
Where,
t- time
i, j, k unit vectors in the direction of x, y, z axis
Formula used:
The relation between displacement is the, 'velocity is the time derivative of displacement'
Similarly relation between displacement and acceleration is,
Step 2
Calculation:
Velocity of the particle is,
Acceleration of the particle is,
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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