Finding Rectangular Coordinates

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Homework Help Overview

The discussion revolves around a particle's motion described by a position vector as a function of time. Participants are exploring how to derive rectangular coordinates for position, velocity, and acceleration at a specific time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to identify the components of the position vector and express them in rectangular coordinates. Questions are raised about the relationships between distance, velocity, and acceleration functions, as well as how to derive these functions from the position vector.

Discussion Status

The discussion is active with participants seeking clarification on the relationships between the different motion functions. Some guidance has been offered regarding the derivation of velocity and acceleration from the position function, but there is no explicit consensus on the approach yet.

Contextual Notes

Participants express uncertainty about the correct interpretation of the position vector components and the process of deriving the associated velocity and acceleration functions. There is a focus on understanding the mathematical relationships involved without providing complete solutions.

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Homework Statement



A particle moves with position as a function of time in seconds given by the vector ~r = (5t^3, 3t − 6t^4)m.

What are the rectangular coordinates of the particle’s position at t = 2.5 s?
What are the rectangular coordinates of the particle’s velocity at t = 2.5 s?
What are the rectangular coordinates of the particle’s acceleration at t = 2.5 s?

Homework Equations





The Attempt at a Solution



I'm a little bit lost? I know that the Vector Components is rx=(5t^3) and ry=6t^4 is that right, so I know I plug in numbers to find the vectors but I don't know which ones?
 
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What's the relationship between distance, velocity and acceleration functions?
 
I'm not sure what that means but it says something like this:

Derive expressions for the velocity and the acceleration of the particle as function of time in
Cartesian coordinates.
 
Yes I am asking if you have a function that tells you distance, how do you get velocity function?, how do you get acceleration function?
 

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