Answer
The proof is detailed below.
Work Step by Step
$$v(s)=k\sqrt s=ks^{1/2}(m/sec)$$ ($k$ is a constant)
Acceleration $a$ is the derivative of velocity $v$ with respect to time $t$. In other words, $$a(t)=\frac{dv}{dt}$$
Applying the Chain Rule: $$a(t)=\frac{dv}{ds}\frac{ds}{dt}$$
Now $ds/dt$, or the derivative of position $s$ with respect to time $t$, is the velocity $v$. $$a(t)=\frac{dv}{ds}\times v=\frac{dv}{ds}\times ks^{1/2}$$
On the other hand, $dv/ds$ is the derivative of $v(s)$ here: $$\frac{dv}{ds}=(ks^{1/2})'=\frac{1}{2}ks^{-1/2}$$
Therefore, $$a(t)=\frac{1}{2}ks^{-1/2}\times ks^{1/2}=\frac{k^2}{2}(m/sec^2)$$
As $k$ is a constant, $a(t)$ is a constant as a result.
