# Kinematics and varying accleration [duplicate]

If accleration varies inversely with square of displacement then how can we find the time it takes to cover distance S?? My attempt I tried to use calculus but didn't, work at all please help.

• See my answer to a similar enough question. And please show your attempt when posting a question. Commented Apr 28, 2017 at 21:33

This doesn't entirely answer the question, but it might help.

As you know, one way of finding the time $t$ is by finding an equation that relates $t$ to any of $a$, $v$ or the displacement $x.$   AFAIK, it doesn't seem obvious to find $t$ without such an equation.

(As you know, since $a$ is not constant, the formulae of UAM won’t work here, even if you know $a$, $v$ and $x$)

Also, to find $v$, you can proceed as follows.

We know

$$a=\frac{1}{x^2}.$$

Then from the relationship $$a=v\frac{dv}{dx},$$ We have $$v\frac{dv}{dx}=\frac{1}{x^2}.$$ You can now find $v$ as a function of $x$ by integrating with respect to $x$.