Question

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 ....... $m / s ^{2}$.

Answer 1

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