# A question in knematics

ritik.dutta3

## 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

## 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.

## Answers and Replies

Gold Member
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!

Gold Member
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.