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

[tarletontexan]

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

 

[fzero]

You're given the position, or displacement, of the object as $$\vec{s}(t) = (x(t),y(t),z(t)).$$ How are the velocity and acceleration related to the position?

 

[tarletontexan]

well they're the derivatives with respect to x...can it really be that simple?

 

[fzero]

You mean derivatives with respect to time I think. Yes, it's kind of simple but it does illustrate a few concepts.

 

[tarletontexan]

well what concepts are those??, I am just a newbie afterall...

 

[fzero]

well what concepts are those??, I am just a newbie afterall...

Vectors and their components, derivatives of common functions, velocity and acceleration.

 

[tarletontexan]

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

 

[fzero]

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.

 

[tarletontexan]

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