Protons and the Heisenberg principle The Heisenberg uncertainty principle implies that it is not possible to calculate the position and velocity of a body at the same time accurately. Electrons follow this principle since their orbitals are just probabilities where they may occur. But in the case of protons, we are kind of certain about their position in the atom. So shouldn't they have a very, very, very high velocity to balance the certainty in position?
You are using the Heisenberg uncertainty principle to relate the uncertainty in position $x$ to the uncertainty in velocity $v$.

However, the quantitative version of this principle actually is

$$\Delta x\cdot\Delta p\geqslant\tfrac12\hbar $$

where $\Delta x$ is the uncertainty in position $x$ and $\Delta p$ is the uncertainty in momentum $p$.

Certainly, since
$$p=m\cdot v$$
or
$$v=\frac pm$$
where $m$ is mass and $v$ is velocity, you may also use the uncertainty principle to compare the uncertainty in position $x$ to the uncertainty in velocity $v$.

However, the mass of a proton is $m_\mathrm p=1.672\,621\,923\,69(51)\times10^{-27}\ \mathrm{kg}$[CODATA2018], whereas the mass of an electron is only $m_\mathrm e=9.109\,383\,7015(28)\times10^{-31}\ \mathrm{kg}$[CODATA2018]; i.e. a proton is over a thousand times heavier than an electron.

Therefore, a given uncertainty in position $x$ and the corresponding uncertainty in momentum $p$ result in a smaller uncertainty in velocity $v$ for the proton.