# How to plot a two-dimensional position vector as function of time?

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.

• See e.g. this answer Finding unit tangent, normal, and binormal vectors for a given r(t) wher you'll find a 3D visualization. You should find a specific questions on this site, I guess it is a duplicate. Mar 19, 2016 at 16:55
• You can use ListPlot[{{x[t],y[t]}}] for plotting a single point in 2d space. Mar 19, 2016 at 19:54

Do you mean something like this?

x[t_] := t^2 - 67;
y[t_] := Sin[t] t^4 + 5 t^2;
Manipulate[
Graphics[Arrow[{{0, 0}, {x[t], y[t]}}], Axes -> True], {t, 0, 3}]


I did it like this because you wanted the position. However, I suggest something that not only you can see the current position, but the plot has the memory of previous positions:

Manipulate[
ParametricPlot[{x[t], y[t]}, {t, 0, tmax}], {tmax, 0.01, 3}]

• Yes, this is what I needed! Mar 20, 2016 at 8:19