Acceleration in Kinematics: How Does it Vary with Displacement?

[ritik.dutta3]

Homework Statement

A particle moves along a straight line such that its displacement x changes with time t as x= sqrt( a^t+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.

 

[adjacent]

The question is incomplete. Please post the full question

 

[ritik.dutta3]

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!

 

[adjacent]

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?

 

[cosmosmike]

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.