Question:
If the velocity of a body related to displacement $x$ is given by $v=\sqrt{5000+24 x} \mathrm{~m} / \mathrm{s}$, then the acceleration of the body is $\ldots \ldots \mathrm{m} / \mathrm{s}^{2}$.
Solution:
$V=\sqrt{5000+24 x}$
$\frac{\mathrm{dV}}{\mathrm{dx}}=\frac{1}{2 \sqrt{5000+24 x}} \times 24=\frac{12}{\sqrt{5000+24 x}}$
$\operatorname{now} a=V \frac{d V}{d x}$
$=\sqrt{5000+24 x} \times \frac{12}{\sqrt{5000+24 x}}$
$\mathrm{a}=12 \mathrm{~m} / \mathrm{s}^{2}$
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