Acceleration in Kinematics: How Does it Vary with Displacement?

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The discussion centers on determining how acceleration varies with displacement for a particle described by the equation x = sqrt(at + 2bt + c). Participants express confusion over the problem's clarity and seek guidance on solving it. The solution involves taking the second derivative of the position function to find acceleration and using the chain rule to relate acceleration to displacement. A suggested method includes calculating dz/dx by deriving dz/dt and dx/dt, followed by substituting x back into the final result. The conversation emphasizes the importance of correctly interpreting the problem and applying calculus techniques.
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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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