For example, it is common to have velocity both as a function of time and of displacement, and use them both at the same time. E.g. $v(x)=.., v(t)=..$
However, this can lead to ambiguity when writing $v(3)=c$, it is unclear whether $t=3$, or $x=3$. I have worked around this by writing things such as $v(x=3)=a$. Is there a conventional notation for this?
There are many notations for this. Say you have a function $f : x, t \mapsto f(x, t)$, then if you fix one of the variables, say $t = t_0$, you can write the function $f : x \mapsto f(x, t_0)$ like this : $$ \boxed{f(\cdot, t_0)}$$
Another solution is to use the fixed variable as an index (underscore in LaTeX) like this : $$ \boxed{f_{t_0}(x)} := f(x, t_0)$$