How to Solve an Object's Velocity and Acceleration Using Vectors?

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Homework Help Overview

The discussion revolves around finding the velocity and acceleration of an object described by its position functions in three-dimensional space, specifically using vector notation. The position is given as a function of time with components in the x, y, and z directions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between position, velocity, and acceleration, noting that velocity and acceleration are derivatives of the position vector with respect to time. There is some uncertainty about the simplicity of the process and the underlying concepts involved.

Discussion Status

Participants are exploring the basic concepts of vector functions and their derivatives. Some guidance has been offered regarding the relationship between position, velocity, and acceleration, but there is still a sense of uncertainty among newer participants about the application of these concepts.

Contextual Notes

One participant mentions that they are working on this problem for extra credit in a college physics class, indicating a potential lack of familiarity with the material. There is also a repeated emphasis on the simplicity of the derivative process, which may suggest a need for further clarification on the concepts involved.

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Homework Statement



an object moves according to x=3m exp(-2/s t), y=4msin(3/s t), z=-5cos(3/s t) find the velocity and the acceleration.

Homework Equations





The Attempt at a Solution


I am unsure what this means, i am doing this for extra credit for my physics class in college(civil engineering major, fresh) and would like an idea as to what i need to do to solve this problem
 
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You're given the position, or displacement, of the object as [tex]\vec{s}(t) = (x(t),y(t),z(t)).[/tex] How are the velocity and acceleration related to the position?
 
well they're the derivatives with respect to x...can it really be that simple?
 
You mean derivatives with respect to time I think. Yes, it's kind of simple but it does illustrate a few concepts.
 
well what concepts are those??, I am just a newbie afterall...
 
tarletontexan said:
well what concepts are those??, I am just a newbie afterall...

Vectors and their components, derivatives of common functions, velocity and acceleration.
 
so your tellin me that these functions are vectors? Ok i can dig it, so i take the derivative with respect to time and i'll have the velocity, take it again and i'll have the acceleration. That seems to be too simple, but i'll try it
 
tarletontexan said:
so your tellin me that these functions are vectors? Ok i can dig it, so i take the derivative with respect to time and i'll have the velocity, take it again and i'll have the acceleration. That seems to be too simple, but i'll try it

What I mean is that the position of the object is a vector whose components are the specified functions. While the concepts are simple, you still have to know that the time derivative of the vector is the vector composed of the derivatives of the components, etc.
 
ok i see where your comin from the derivative of the vector with respect to time is the vector with the derivatives of the components with respect to time
 

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