> Q. If the velocity of a particle is given by $ v={{(180-16x)}^{1/2}},m/s $ . then its acceleration will be – LIVE ANSWER TODAY

Q. If the velocity of a particle is given by $ v={{(180-16x)}^{1/2}},m/s $ . then its acceleration will be

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If the velocity of a particle is given by $ v={{(180-16x)}^{1/2}},m/s $ . then its acceleration will be

Solution:

$a =frac{ d v }{ d t }=frac{ d x }{ d t } frac{ d v }{ d x }= v frac{ d v }{ d x }$

$v=(180-16 x)^{frac{1}{2}}$

$v^{2}=180-16 x$

$text { Diff. both sides wrt. } x text { , we get: }$

$2 v frac{d v}{d x}=-16$

$v frac{ d v }{ d x }= a =- 8 , m / s ^{2}$

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