I got to a point where I have $x$ and $y$ coordinates of a position vector written as a function of time.
x[t_]:=t^2-67; y[t_]:= Sin[t] t^4 + 5 t^2;
Now my idea was to somehow use
Manipulate so that I could animate how the position of point $(x(t),y(t))$ changes in a two-dimensional space with time.
I was able to use Manipulate and plot $x$ or $y$ coordinates separately but I can't get any further. I got an idea to discretize the time domain and than use Manipulate with combination of ListPlot or something, yet I would like to stay in the continuous case if possible.