The velocity (v) of a particle moving along x | vedclass

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Question

(d)

$a=\frac{v d v}{d x}$

$\frac{d v}{d x} \rightarrow$ slope

So, $\frac{-4}{2}=-2$

Intercept $=+4$

$a \rightarrow$ Negative

So, $a=

Vedclass · Accepted Answer

$a=4 x-8$

Vedclass · Answer

(d)

$a=\frac{v d v}{d x}$

$\frac{d v}{d x} \rightarrow$ slope

So, $\frac{-4}{2}=-2$

Intercept $=+4$

$a \rightarrow$ Negative

So, $a=\frac{v d v}{d x}$

Relation between $V$ and $x$

$\Rightarrow \frac{v-4}{x-0}=\frac{0-4}{2-0}$

$\Rightarrow \frac{v-u}{x}=\frac{-4}{2}$

$\Rightarrow v-4=-2 x$

$\Rightarrow v=-2 x+4$

$\Rightarrow \frac{d v}{d x}=-2$

$\Rightarrow a=\frac{v d v}{d x}=(-2 x+4)(-2)$

$\Rightarrow a=4 x-8$

The velocity $(v)$ of a particle moving along $x$-axis varies with its position $x$ as shown in figure. The acceleration $(a)$ of particle varies with position $(x)$ as

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