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I've been doing more mechanics recently - further kinematics in M3. I've come across another question i'm confused by.

A particle moves on the positive x-axis. When its displacement from O is x meters, is acceleration is of magnitude x^-3 m/s^2 and directed towards O. Given that initially, when t=0, the particle is at rest with x=1, find the time the particle takes to reach x=1/4.

First i integrate with respect to x to find:

V^2 = x^-2 + C where C = -1

v^2 = x^-2 -1

V = x^-1 - 1

Now i integrate again to find velocity as (dx/dt):

dx/dt = x^-1 - 1

Which is a FODE, however i cant solve it.

Thank you,

Bob

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# Homework Help: Yet another FODE question

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