Question

solution pls
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Answer 1

$\frak{Given} \begin{cases} \sf{Mass\ =\ 10\ kg} \\ \\ \sf{Velocity\ =\ 10 \sqrt{x}} \end{cases}$

$\underline{ \mathfrak{ \: To\:Find:- \: }}$

•$\sf Work \:down(W)$

$\underline{ \mathfrak{ \: Solution :- \: }}$

$\sf At \:first\:we\:need\:to\:find\:acceleration$

$\sf Here \:Given:-$

$\sf v = 10√x$

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$\dashrightarrow \bf{a\ =\ \dfrac{dv}{dt}} \\ \\ \dashrightarrow \tt{a\ =\ \dfrac{dv}{dt}\ \times\ \dfrac{dx}{dx}} \\ \\ \dashrightarrow \tt{a\ =\ \dfrac{dx}{dt}\ \times\ \dfrac{dv}{dx}} \\ \\ \dashrightarrow \tt{a\ =\ v \dfrac{dv}{dx}} \\ \\ \dashrightarrow \tt{a\ =\ 10 \sqrt{x} \dfrac{d(10 \sqrt{x})}{dx}} \\ \\ \dashrightarrow \tt{a\ =\ 10 \sqrt{x} \dfrac{10}{2 \sqrt{x}}} \\ \\ \dashrightarrow \tt{a\ =\ 10 \cancel{\sqrt{x}} \dfrac{5}{\cancel{\sqrt{x}}}} \\ \\ \dashrightarrow \tt{a\ =\ \dfrac{50}{1}}$

$\dashrightarrow {\boxed{\frak{\purple{a= 50\;ms^{-2}}}}}$

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$\sf Again$

$\dashrightarrow \bf{W\ =\ F.dx} \\ \\ \\ \dashrightarrow \tt{W\ =\ ma.dx} \\ \\ \\ \dashrightarrow \tt{W\ =\ 10\ \times\ 50\ .dx} \\ \\ \\ \dashrightarrow \tt{W\ =\ 10(50.dx)}$

$\displaystyle \dashrightarrow \tt{\int W\ =\ 10 (\int_4 ^9 50.dx)} \\ \\\dashrightarrow \tt{W\ =\ 10( \big[ 50x \big] ^9 _4)} \\ \\ \dashrightarrow \tt{W\ =\ 10(50 [9\ -\ 4]) } \\ \\ \dashrightarrow \tt{W\ =\ 10( 50[5])}$

$\dashrightarrow {\boxed{\frak{\purple{W= 2500\;J}}}}$

ㅤ$\;\;\underline{\textbf{\textsf{Hence -}}}$

$\underline{\textsf{ Work down </p><p>\textbf{ 2500J}}}.$

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