Newton's Second Law gives the definition of Force.
The rate of change of momentum with respect to time is Force
In Mathematical Form,
$\vec{F}=\frac{d \vec{p}}{d t}$
where $\vec{p}$ is momentum.
since we write $\vec{p}=m \vec{v},$ we can write Force as$:$
$F=m \frac{d \vec{v}}{d t}$
We are given velocity here.
$v=\ln x m / s$
We need to differentiate it with respect to time. But velocity is given as a function of position. So we differentiate it as follows$:$
$v=\ln x$
$\Longrightarrow \frac{d v}{d t}=\frac{d}{d x}(\ln x) \times \frac{d x}{d t}$
$\Longrightarrow \frac{d v}{d t}=\frac{1}{x} \times v$
$\Longrightarrow \frac{d v}{d t}=\frac{1}{x} \times \ln x$
$\Longrightarrow \frac{d v}{d t}=\frac{\ln x}{x}$
Now, we have to find where force is zero.
$F=0$
$\Longrightarrow m \frac{d v}{d t}=0$
$\Longrightarrow m \times \frac{\ln x}{x}=0$
$\Longrightarrow \frac{\ln x}{x}=0$
$\Longrightarrow \ln x=0$
$\Longrightarrow \quad x=1 m$
Thus, Force becomes zero at $x=1 \mathrm{m}$