1. We are given velocity as a function of displacement:

$v = \sqrt{5000 + 24x}$

We need to find acceleration $a$.

2. Use the kinematic relation:

$a = \frac{dv}{dt} = \frac{dv}{dx}\cdot\frac{dx}{dt} = v\frac{dv}{dx}$

3. Differentiate $v$ with respect to $x$:

$v = (5000+24x)^{1/2}$

So,

$\frac{dv}{dx} = \frac{1}{2}(5000+24x)^{-1/2}\cdot 24$

$\frac{dv}{dx} = \frac{12}{\sqrt{5000+24x}}$

4. Now multiply by $v$:

$a = v\frac{dv}{dx}$

$a = \sqrt{5000+24x}\cdot \frac{12}{\sqrt{5000+24x}}$

$a = 12\ \text{m/s}^2$

5. Hence, the acceleration is constant.

$\boxed{12}$