Question

For a body traveling with uniform acceleration its final velocity v is
$\sqrt{180 - 7x}$
where x is distance travelled. Then the acceleration is​

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

Final velocity of a body travelling with uniform acceleration is provided.

$\dag\:\boxed{\bf{\red{v=\sqrt{180-7x}}}}$

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find acceleration of body.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

$:\implies\sf\:v=\sqrt{180-7x}$

Squaring both sides,

$:\implies\sf\:v^2=180-7x$

Differentiating both sides wrt t,

$:\implies\sf\:2v\:\dfrac{dv}{dt}=0-7\:\dfrac{dx}{dt}$

$:\implies\sf\:2v\:\dfrac{dv}{dt}=-7v\:\:{\large(}\because\dfrac{dx}{dt}=v{\large)}$

$:\implies\sf\:2v\times a=-7v\:\:{\large(}\because\dfrac{dv}{dt}=a{\large)}$

$:\implies\sf\:a=-\dfrac{7v}{2v}$

$:\implies\underline{\boxed{\bf{\purple{a=-3.5\:ms^{-2}}}}}\:\gray{\bigstar}$

God_Bless :)