If velocity of a body related to displacement {x} is given by v=√{5000+24 {x}} {m} / {s} , then ac

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2.Motion in Straight Line

hard

If the velocity of a body related to displacement ${x}$ is given by $v=\sqrt{5000+24 {x}} \;{m} / {s}$, then the acceleration of the body is $\ldots \ldots {m} / {s}^{2}$

A$12$

B$16$

C$8$

D$24$

(JEE MAIN-2021)

Solution

${V}=\sqrt{5000+24 {x}}$
$\frac{{d} {V}}{{dx}}=\frac{1}{2 \sqrt{5000+24 {x}}} \times 24=\frac{12}{\sqrt{5000+24 {x}}}$
$\text { now } {a}={V} \frac{{dV}}{{dx}}$
$\quad=\sqrt{5000+24 {x}} \times \frac{12}{\sqrt{5000+24 {x}}}$
$\qquad {a}=12 {m} / {s}^{2}$

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