Vector algebra - The velocity is given by

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Homework Help Overview

The problem involves vector algebra, specifically focusing on the relationship between velocity, position, and acceleration of an object over time. The velocity functions are provided, and the task is to determine the position at a specific time and the instantaneous acceleration at another time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between position, velocity, and acceleration, with one participant attempting to compute velocity directly from the given functions. Others suggest using calculus to derive acceleration and integrate for position.

Discussion Status

The discussion includes attempts to clarify the relationships between the different physical quantities involved. Some guidance has been offered regarding the use of derivatives and integrals, but there is no explicit consensus on the approach to take.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an initial position provided, but the implications of that in the context of the problem are still being explored.

lilyE
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Homework Statement


The velocity of an object as a function of time is given by:

Vx(t) = 12t2 - 5t + 40 m/s
Vy(t) = 5t - 30 m/s

What is position at 2 sec if the object has an initial position of x = 5 m and y = 8 m?
What is the instantaneous acceleration at 10 s?

Homework Equations

The Attempt at a Solution


I started by just plugging time (2 sec) into the equation to get the velocity and then writing that out in component form (V = Vxi + Vyj = 78i - 20j), but it asks for position/acceleration and I'm not entirely sure how to go about solving for that.
 
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Take the derivative to get the acceleration. Integrate to get the position.
 
How are position, velocity, and acceleration related? Hint: Calculus!
 
Thank you! I think I've got it now.
 

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