Acceleration in Kinematics: How Does it Vary with Displacement?

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Homework Help Overview

The discussion revolves around a kinematics problem involving a particle's displacement as a function of time, specifically examining how acceleration varies with displacement. The displacement is given by the equation x = sqrt(at + 2bt + c), where a, b, and c are constants.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore how to derive acceleration from the given displacement function, with some questioning the completeness of the problem. Others suggest using derivatives to find acceleration and discuss the relationship between acceleration and displacement.

Discussion Status

The discussion is ongoing, with participants providing various approaches to derive acceleration from the displacement function. Some guidance has been offered regarding the use of derivatives, but no consensus has been reached on the method or final expression.

Contextual Notes

There is a noted concern about the clarity of the problem statement, with some participants seeking further details to ensure a complete understanding of the task at hand.

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Homework Statement



A particle moves along a straight line such that its displacement x changes with time t as x= sqrt( at+2bt + c) where a, b and c are constants, then the acceleration varies with x as

Homework Equations





The Attempt at a Solution


I can't figure out how do i solve it. Using graphs as well, I could not arrive at any conclusion.
 
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The question is incomplete. Please post the full question
 
No, @adjacent, the question isn't incomplete. We have to fill in the blank. "the acceleration varies with x as ________ ". Sorry for not mentioning it clearly!
 
ritik.dutta3 said:
No, @adjacent, the question isn't incomplete. We have to fill in the blank. "the acceleration varies with x as ________ ". Sorry for not mentioning it clearly!

When you are given the position as a function of time, how do you find the acceleration using derivative?
 
My suggestion:
First take second derivative of x with respect to t to get acceleration which we will call z.
Then use dz/dx = (dz/dt)/(dx/dt)

Looks messy, but technically correct. In the final result, substitute for x where it appears.
 

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