A body moves with velocity v = ln x m/s where | vedclass

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Question

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}=

Vedclass · Accepted Answer

$x = 1\,\, m$

Vedclass · Answer

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$:$

$v=\ln x$

$\Longrightarrow \frac{d v}{d t}=\frac{d}{d x}(\ln x) 	imes \frac{d x}{d t}$

$\Longrightarrow \frac{d v}{d t}=\frac{1}{x} 	imes v$

$\Longrightarrow \frac{d v}{d t}=\frac{1}{x} 	imes \ln x$

$\Longrightarrow \frac{d v}{d t}=\frac{\ln x}{x}$

Now, we have to find where force is zero.

$F=0$

$\Longrightarrow m \frac{d v}{d t}=0$

$\Longrightarrow m 	imes \frac{\ln x}{x}=0$

$\Longrightarrow \frac{\ln x}{x}=0$

$\Longrightarrow \ln x=0$

$\Longrightarrow \quad x=1 m$

Thus, Force becomes zero at $x=1 \mathrm{m}$

A body moves with velocity $v = ln x\ m/s$ where $x$ is its position. The net force acting on body is zero at