If the velocity of a body related to displacement x is given by $\mathrm{v}=\sqrt{5000+24\mathrm{x}} \mathrm{m}/\mathrm{s}$, then the acceleration of the body is ...... m / s².

Velocity of body is

              $\mathrm{v}=\sqrt{5000+24\mathrm{x}}\mathrm{m}/\mathrm{s}$

Acceleration of body can be calculated as

$\begin{array}{l} \mathrm{a}=\frac{\mathrm{dv}}{\mathrm{dt}}=\frac{\mathrm{dv}}{\mathrm{dx}}\times \frac{\mathrm{dx}}{\mathrm{dt}}\\ \Rightarrow \mathrm{a}=\mathrm{v}\frac{\mathrm{dv}}{\mathrm{dx}} ...\left(\mathrm{i}\right)\\ \frac{\mathrm{dv}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}}\left(\sqrt{5000+24\mathrm{x}}\right)\\ \Rightarrow \frac{\mathrm{dv}}{\mathrm{dx}}=\frac{1}{2\left(\sqrt{5000+24\mathrm{x}}\right)}\times 24\\ =\frac{12}{\sqrt{5000+24\mathrm{x}}}\end{array}$

Substituting the value of $\frac{\mathrm{dv}}{\mathrm{dx}}$ in Eq. (i), we get

           $\begin{array}{l}\mathrm{a}=\sqrt{5000+24\mathrm{x}}\times \frac{12}{\sqrt{5000+24\mathrm{x}}}\\ =12\mathrm{m}/{\mathrm{s}}^2\end{array}$

Thus, the acceleration of body is 12 m/s².