calcuate vector valued functions and take derivatives

I'm sure this is anything but new however I keep plugging away at these kind of issues to no avail so here we go

I get approached with a simple 2d function...... say x(t) = 2.4t and y(t) = 3 - 1.2 t^2

or maybe a position function R = [4 + (2.5)t^2]i + (5)tj it seems easy enough to plot this as a parametric function using t = linspace() but how would I go about defining this as a single function and say calculate t = 2 that gives me an i and j vector that I can use to calc the resultant vector and the direction (angle) of that vector.... I should be able to take a derivative of R and calc the velocity as well.. I continually find myself needing to do this but unable to get in my head how to do it effectively